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GIFT  OF 
Publisher 


Education  dept. 


iJKNGE  LIBRAF 

UNIVERSITY  Or    C-ki_1>  C.v.iiA 
BERKELEY.  CALIFORNIA 


WHEELER'S   GRADED 
ARITHMETICS 


BY 


FREDERICK   H.   SOMERVILLE 

Formerly  of  the  Lawrenceville  School  and  the 

William  Penn  Charter  School 

Philadelohia 

AND 

ELLIS  U.  GRAFF 

Superintendent  of  Schools 
Indianapolis 


ADVANCED   BOOK 


CHICAGO 
W.   H.  WHEELER   &l  COMPANY 


-7?  m<^r.  .J2mt 

Copyright,  1919, 
By  WILLIAM  H.  WHEEI  ER 


PREFACE 

The  leading  courses  in  arithmetic  for  the  Seventh  and  Eighth 
grades  apply  elementary  principles  to  actual  business  problems, 
and  they  recommend  that  good  teaching  shall  combine  a  certain 
amount  of  general  information  with  a  good  working  knowledge  of 
business  forms.  In  recent  years  these  courses  have  recognized 
the  necessity  iox  coordinating  practical  arithmetic  with  the  prob- 
lems of  home  economics,  while  manual  training,  domestic  science, 
and  agriculture  have  been  included  as  imperative  essentials. 
Manifestly,  therefore,  a  well-planned  text  designed  for  the  last 
two  years  of  the  elementary  schools  must  meet  all  of  the  older  re- 
quirements, and,  at  the  same  time,  provide  adequate  material 
for  the  broadening  influences  that  seek  to  vitalize  modern  teach- 
ing. The  authors  feel  that  this  third  book  of  the  series  meets 
both  the  old  and  the  new  demands. 

While  it  is  true  that  the  methods  of  all  business  and  manufac- 
turing firms  develop  certain  details  of  form  that  are  not  found  in 
school  textbooks,  it  is  also  true  that  these  details  are  merely 
variations  which  extend  beyond  the  fundamentals  that  the  school 
must  thoroughly  teach.  The  keen  business  man  does  not  expect 
young  boys  and  girls  to  have  a  knowledge  of  business  practice; 
but  he  has  the  right  to  expect  that  they  shall  be  habitually  careful, 
systematic,  and  accurate.  Consequently,  the  textbook  and  the 
teacher  must  unswervingly  concentrate  on  the  development  of 
these  qualities  in  order  to  render  the  best  service  for  both  the 
pupil  and  the  future  employer. 

This  book  covers  a  wide  range  of  modern  arithmetical  applica- 
tions. Briefly,  but  in  all  essential  details,  it  treats  General  Bank- 
ing, Savings  Banks,  Federal  Reserve  Banks,  Liberty  Loan  In- 
vestments, Mortgages,  Building  and  Loan  Associations,  General 

3 

611196 


4  •  PREFACE 

Business  Forms,  Insurance,  and  Taxation.  It  also  devotes  un- 
usual space  to  the  Problems  of  the  Home ;  giving  extended  treat- 
ment to  the  ''Budget  Plan";  to  the  relative  expense  of  owning  or 
renting  property;  to  problems  of  furnishing  and  maintaining  a- 
home ;  and  to  the  teaching  of  practical  Thrift  and  Economy. 
Furthermore,  it  covers  the  ordinary  problems  of  Manual  Training, 
and,  under  Additional  Topics  for  Study  and  Reference,  provides 
certain  work  that,  at  the  discretion  of  the  teacher,  may  be  treated 
as  essential  where  a  prescribed  course  demands  it. 

The  book  is  purposely  limited  to  recognized  essentials,  and  it 
intentionally  avoids  certain  tendencies  and  theories  which,  while 
attractive  as  experiments,  have  not  yet  established  themselves 
as  a  part  of  practical  arithmetic.  The  authors  have  endeavored  to 
give  a  practical  foundation,  to  provide  simple  methods,  and  to 
confine  concrete  problems  to  those  which  actually  occur  in  average 
home  and  business  life  ;  and  they  believe  that  all  obsolete  topics 
have  been  eliminated,  that  the  book  gives  an  interesting  trans- 
formation from  abstract  to  applied  arithmetic,  and  that  it  will  be 
a  definite  preparation  for  the  everyday  problems  of  the  child's  life. 

The  authors  gratefully  acknowledge  their  indebtedness  to  the 
teachers  who  have  given  helpful  criticisms,  and  to  the  business 
men  who  have  aided  them  by  the  contribution  of  accurate  infor- 
mation and  expert  suggestions. 


CONTENTS 


SEVENTH  YEAR 


PAGE 

Business  Forms   ....  7 

The  Cash  Account    ...  7 

Bills 9 

Practical  Measurements    .     .  13 

Surface  Measures      ...  13 

The  Builder's  Applications  13 

Lumber 13 

Flooring 15 

Roofing 16 

Lathing 18 

Plastering 19 

Painting 20 

The  Householder's  Applica- 
tions       22 

Papering 22 

Carpeting     ....  24 
The  Contractor's  Applica- 
tions       26 

Paving 26 

Volume  Measures      ...  28 
The  Farmer's  Applications  28 
Wood  Measure ....  28 
Capacity  of  Bins        .     .  29 
The  Coretractor's  Applica- 
tions       29 

Excavations .     .          .     .  30 

Brickwork     ....  31 

Concrete 33 

Stonework         ....  34 

Saving       and       Investing 

Money .     .     .     .     .     .  36 

The  War  Savings  Plan    .  36 


Solution  by  Analysis 
Oral  Analysis  .  . 
Written  Analysis  . 


The  Equation 

Solving  Problems  by  Equa- 
tions      


Percentage      .... 

The  First  Problem 
The  Second  Problean 
The  Third  Problem 
Applications     . 
Profit  and  Loss 
Applications     . 
Marking  Good^ 
Retail  Merchant's  ^lethod 
Comme-cial  Discount    . 

Applications 

Discount  Se:'ies     .... 
Applications  to  B'lls      •     . 


PAGE 

38 
38 
42 

48 

53 

58 
61 
64 

68 
73 

77 
80 
82 
84 
86 
88 
91 
93 

95 


Interest  

Method  of  Years   Months, 

and  Davs  ...  .96 

Method  on  Principal  of  $1  .  97 

Exact  Interest 100 

Banker's  Time      ....  102 

Interest  Tables      ....  103 

Saving  and  Investing  Money  105 

The  Savings  Banks    ...  105 

The  Liberty  Loan  Bonds    .  107 


6 


CONTENTS 


EIGHTH  YEAR 


Banking 

Opening  an  Account 
The  Bank  Check  .  . 
Bank  Discount  .  . 
Compound  Interest  . 
Savings  Banks  .  . 
Federal  Reserve  Banks 


Exchange    

Postal  Money  Order 
Express  Money  Order 
Telegraph  Money  Order 
Personal  Check 
Bank  Draft       .     . 
Sight  Draft       .     . 


Ratio  and  Proportion 

Ratio 

Proportion  .     .     . 

Powers 


Roots      .     .     .     ,     . 

Square  Root     .     . 

The  Right  Triangle  . 
The  Diagonal  of  a  Squar 

The  Circle 

Length  of  Circumference 
Area  of  a  Circle    . 


The  Cylinder  .... 

The  Volume  of  a  Cylinder 
Capacity  of  Silos  .     . 
Capacity  of  Tanks  . 

Business  Forms   . 
Accounts      .... 
The  Day  Book      .     . 
The  Ledger .... 

Bills 

Receipts 

The  Parcel  Post    .     . 

Insurance   

Property  Insurance   . 
Life  Insurance .     .     . 


PAGE 

109 
110 
112 
115 
120 
124 
126 

128 
129 
130 
131 
132 
133 
134 

138 
138 
142 

148 

150 
152 

159 
161 

165 
165 
166 

170 
170 
172 
173 

175 
175 
176 
177 
179 
182 
183 

185 
185 

188 


Taxes 


PAGE 

192 


Mortgages 198 


Building   and   Loan   Associa 
tions 


Stocks  and  Bonds     . 
Buying  and  Selling    .     . 
To  Find  the  Cost  of      . 
To  Find  Receipts      .     . 
Calculating  Profit  and  Loss 
Bonds 

Practical       Applications      of 

Arithmetic      .     .     .     . 

Problems  in  the  Home  .     . 

House  Accounts     .     .     . 

The  Budget  Plan  .     .     . 

Cost  of  Owning  Com- 
pared with  Cost  of 
Renting 

Cost  of  Furnishing     .     . 

Cost  of  Maintaining  .  . 
Gas  Lighting  .  .  . 
Electric  Lighting    .     . 

Kitchen  Measures  and 
Costs 

Economy  in  Buying  .     . 

Menus  and  their  Costs  . 
Problems  in  Manual  Train- 


ing 


Estimating  Lumber  Bills 
Constructing  Shapes  .     . 

Additional  Topics  for  Study  and 
Reference  .     .     . 

Measurement  of  SoUds 
Promissory  Notes 
Partial  Payments 
Longitude  and  Time 
Public  Lands    .     .     . 
Metric  System      .     . 
Cube  Root  .... 


Index 


199 

201 
202 
204 
205 
207 
208 

212 
212 
212 
213 


215 
217 
219 
219 
220 

221 
223 
224 

226 
226 

228 

231 
231 
245 
248 
253 
260 
262 
276 

283 


•>  ^  »  » 

3      1 


.% :'' 


SEVENTH   GRADE 

BUSINESS    FORMS 

I.  The  Cash  Account.  A  Cash  Account  is  a  record  of  the  money 
received  and  of  the  money  paid  out  by  an  individual  or  a  firm. 

Usually  two  pages  are  used  for  a  cash  account.  On  the  left  page 
the  amounts  of  cash  received  are  written,  and  on  the  right  page  the 
different  amounts  of  each  paid  out  are  written.  A  cash  account  is 
balanced  when  the  difference  between  the  cash  received  and  the 
cash  paid  out  equals  the  cash  on  hand  or  in  the  bank.  Some 
cash  accounts  are  balanced  at  the  end  of  each  month,  others  at 
the  end  of  each  week,  but  most  business  firms  balance  their  cash 
accounts  daily. 

The  side  of  the  cash  account  upon  which  the  cash  received  is 
recorded  is  called  the  Debit  Side.  The  side  upon  which  the  cash 
paid  out  is  recorded  is  called  the  Credit  Side. 


8  BUSINESS  FORMS 

The  usual  method  of  keeping  a  personal  cash  account  is  shown 
in  the  illustration. 

Explanation  :  On  the  debit  side  are  entered  the  amount  of  cash 
on  hand  at  the  beginning  of  the  month  and  every  item  of  cash 
received  thereafter. 

1.  The  balance  left  over  from  the  preceding  week. 

2.  An  interest  check  received  for  the  use  of  a  loan. 

3.  The  receipts  from  the  sale  of  a  bicycle. 

4.  The  weekly  wages  of  the  man  keeping  the  account. 

On  the  credit  side  there  are  entered  his  expenses  for  the  week. 
To  balance  the  account : 

1.  Add  the  amounts  on  the  debit  side. 

2.  Add  the  amounts  on  the  credit  side. 

3.  Subtract  the  second  sum  from  the  first  sum. 

The  difference  is  the  balance,  or  the  Cash  on  Hand. 

WRITTEN    APPLICATIONS 

Prepare  a  sheet  ruled  to  represent  two  pages  like  those  in  the 
illustration,  and  on  this  sheet  write  cash  accounts  for  the  con- 
ditions given  below. 

1.  John  Fox  works  for  his  father  on  the  farm.  He  receives  from 
his  father  a  weekly  wage  of  $5.00,  and  it  is  agreed  that  he  is  to 
have  one  half  of  the  amount  received  from  the  sale  cf  young 
stock,  and  that  he  is  to  pay  one  fourth  of  the  expense  for  seed. 
The  items  to  be  entered  for  the  first  week  of  John's  cash  account 
are:  May  1,  cash  on  hand,  $7.50;  May  3,  received  wages, 
$5.00 ;  May  5,  share  from  sale  of  calf,  $3.50 ;  May  9,  butternuts 
sold,  $1.15;  May  2,  paid  for  shoes,  $2.50;  May  3,  paid  for  seed 
corn,  $2.50 ;  May  8,  paid  for  magazine,  $.25. 

2.  Mr.  Charles  Hunt  is  a  clerk  in  a  city  store  and  lives  in  a  near- 
by suburban  town.     His  cash  account  for  one  week  includes  the 


THE  CASH  ACCOUNT  9 

following  items :  August  5,  Cash  on  hand,  $42.75 ;  August  6, 
received  commissions  for  one  week,  $4.10;  August  6,  paid  for 
commutation  ticket,  $5.90;  August  8,  paid  for  board,  $4.50; 
August  9,  paid  for  1  dozen  collars,  $1.50,  1  pair  rubbers,  $1.00, 
book,  $1.12,  club  dues,  $10.00;  August  10,  received  one  week's 
salary,  $21.00;  August  11,  paid  room  rent,  $2.50,  paid  laundry- 
bill,  $1.18. 

3.  Tom  French  is  an  amateur  photographer,  and  the  following 
are  his  receipts  and  expenses  for  making  four  dozen  photographs 
of  the  school  football  team.  Nov.  1,  3  plates  at  5c^  each;  de- 
veloper, 5^;  hyposulphite,  10^;  4  dozen  mounts  at  15^^  a  dozen; 
5  dozen  sheets  of  printing  paper  at  35  ff  a  dozen ;  received  on 
November  20,  10^  each  for  48  photographs.  Find  the  amount 
of  his  profit. 

4.  Robert  Coleman  has  20  hens,  and  for  the  month  of  January 
his  receipts  and  expenses  were  as  follows :  January  2,  paid  for 
3  bushels  of  corn  at  $.90  per  bushel ;  received  45^  a  dozen  for  2 
dozen  eggs ;  January  8,  paid  5^  a  pound  for  25  pounds  of  bone 
meal ;  January  9,  received  48ff  a  dozen  for  2  dozen  eggs ;  January 
15,  paid  10^  a  pound  for  3  pounds  of  grit ;  January  16,  received 
50^  a  dozen  for  4  dozen  eggs ;  January  23,  paid  $.75  for  white- 
washing henhouse ;  January  30,  received  47f!f  a  dozen  for  4  dozen 
eggs.     Find  the  amount  of  his  profit  for  the  month. 

n.  Bills.  A  Bill  is  a  written  statement  of  goods  sold,  giving 
the  date  of  the  sale,  the  quantity  sold,  the  prices  per  unit  of  quan- 
tity, and  the  total  amount  of  the  sale  when  the  different  items  are 
included. 

When  a  bill  is  paid  the  person  receiving  'the  payment  writes 
"  Paid  "  or  "  Received  Payment  "  at  the  bottom  of  the  sheet, 
and  signs  his  name.  This  is  called  receipting  a  bill.  If  an  em- 
ployee signs  a  receipt  for  his  firm,  he  writes  the  firm's  name  and 
then  writes  his  own  name  or  initials  underneath. 


10 


BUSINESS  FORMS 


Nashville, Tenn.. 


.19_ 


M 


BOUGHT  OF 

CHARLES  E.AUSTIN 
GROCER 

Phone  4715  5284  Main  street 


The   Grocer's    Memorandum. 

This  is  one  of  the  simplest  forms 
of  a  bill.  The  illustration  shows 
a  form  of  memorandum  used  by 
many  grocers.  This  is  usually 
sent  to  a  customer  with  the 
delivery  of  her  order.  By  this 
means  she  is  kept  informed  of 
each  daily  transaction,  and  the 
bill  also  serves  as  a  check  upon 
the  order  of  groceries  delivered. 


WRITTEN  APPLICATIONS 

Prepare  memoranda  for  each  of  the  following,  using  your  own 
name  as  the  purchaser  and  the  name  of  your  local  grocer  as  the 
seller. 

1.  On  August  4  you  purchased  groceries  as  follows :  5  pounds 
of  sugar  for  $.38;  5  pounds  of  lard  for  $.70;  6  bars  of  soap  for 
$.30;  1  quart  of  molasses  for  $.25;  2  pounds  of  rice  for  $.36; 
1  sack  of  flour  for  $1.40;  1  can  of  soup  for  $.12. 

2.  On  August  10  you  bought  the  following:  12-pound  sack 
flour,  $.60;  5  pounds  rice,  $.35;  4  bars  soap,  $.30;  1  bushel 
potatoes,  $1.25;  1  pound  cocoa,  $.35;  1  quart  olive  oil,  $.80; 
3  pkgs.  corn  flakes,  $.30. 

3.  On  September  4  your  purchases  were  2  pounds  beefsteak 
at  $.35;  3  pkgs.  oatmeal  at  $.10  each;  1  bottle  bluing  at  $.15; 
1  bottle  vanilla  at  $.45;  3  pounds  rice  at  $.18;  4  pounds  starch 
at  $.10;  and  1  bushel  potatoes  at  $.95. 

4.  The  American  Hotel  orders  the  following  from  the  grocer  on 
July  10:  15  pounds  chops  at  $.30;  10  pounds  cornmeal  at  $.08; 
100  bars  soap  at  $.04 ;  5  dozen  Dutch  Cleanser  at  $.95  per  dozen ; 
20  pounds  cocoa  at  $.27  per  pound ;  100  pounds  coffee  at  $.28  per 
pound ;  and  1  dozen  pkgs.  table  salt  at  $.20. 


BILLS 


11 


The  simple  form  of  bill  given  below  is  in  common  use.     Several 
other  forms  are  used,  but  all  of  them  are  similar  to  this  one. 


TERMS:   Cash 


PHILADELPHIA. 


.19 


PILLSBURY  FURNITURE  CO. 

DEALERS     IN 

Fine  Furniture,  Rugs  and  Draperies 


Sold  to. 


WRITTEN   APPLICATIONS 

Make  a  neat  copy  of  the  billhead  illustrated  above,  and  make 
out  bills  for  the  sales  in  the  exercises  given  below.  In  each  case 
receipt  the  bill,  signing  the  firm  name  and  your  own  initials. 

1.  On  July  10,  1918,  James  Robinson  purchased  from  the 
Pillsbury  Furniture  Company  6  dining-room  chairs  at  S5.50; 
1  buffet  at  $75.00;  and  1  Axminster  rug  at  $42.50.  Make  out 
the  bill  as  directed  above. 

2.  On  the  12th  of  October,  1918,  the  Sterlington  Hotel  pur- 
chased of  the  Pillsbury  Furniture  Company  the  following :  24 
brass  beds  at  $16.25;  24  bureaus  at  $21.50;  24  chiffoniers  at 
$15.75 ;  and  24  Brussels  rugs  at  $19.40.  On  the  following  day 
they  also  purchased  145  yards  of  Axminster  carpet  at  $1.10  a 
yard.     Make  out  a  bill  of  these  items  and  receipt  it. 


12  BUSINESS  FORMS 

3.  Mr.  Charles  E.  Wilson  bought  furniture  from  the  Pillsbury 
Company  as  follows :  1  dining-room  table,  $45.00 ;  8  dining-room 
chairs  at  $7  each;  1  buffet,  $87.50;  1  serving  table,  $35;  1  rug, 
$52.50;  1  library  3-piece  suite,  $115;  1  library  table,  $45;  1 
mahogany  rocker,  $21 ;  1  wicker  rocker,  $13.50 ;  1  Axminster 
rug,  $67.50;  1  Wilton  velvet  rug,  $87.50;  and  1  hall  runner  6 
yards  long  at  $2.25  per  yard.  Make  out  a  bill  and  receipt  it  for 
the  firm. 

4.  The  Hub  Clothing  Co.  bought  the  following  from  Rogers, 
Richardson  &  Co.:  50  men's  overcoats  at  $17.50;  150  men's  suits 
at  $21.50;  200  boy's  suits  at  $6.75;  150  young  men's  suits  at 
$18.75;  and  300  knit  sweaters  at  $4.20.  Make  out  a  bill  head  and 
fill  in  these  items.  Show  that  it  was  paid  30  days  after  it  was 
dated,  and  that  the  firm  name  was  signed  by  the  cashier, 
J.  E.  Harris. 

5.  Finley,  Houston  &  Co.,  of  Cleveland,  Ohio,  are  wholesale 
dealers  in  women's  clothing.  Make  out  a  bill  for  the  items  given 
below,  and  show  that  the  goods  were  bought  by  Miller  and 
FuUerton  of  Columbus,  Ohio,  on  March  1,  1919,  and  that  the  bill 
was  paid  March  10.  50  doz.  suede  gloves  at  $15.50;  300  pr.  silk 
hose  at  $1.25 ;  125  Georgette  crepe  blouses  at  $3.25 ;  60  serge  capes 
at  $13.75;  48  Foulard  dresses  at  $21.50;  and  200  gingham  house 
dresses  at  $3.75. 

6.  Make  out  a  bill  in  which  you  are  the  purchaser  of  the  follow- 
ing goods  :  10  tennis  nets  at  $4.50  each  ;  6  tennis  rackets  at  $4.75 
each;  5  golf  clubs  at  $3.25  each;  10  baseball  bats  at  $.75  each; 
5  doz.  baseballs  at  $9.00  per  doz. ;  4  catcher's  gloves  at  $4.25  each  ; 
10  fielder's  gloves  at  $2.35  each ;  3  catcher's  pads  at  $4.75  each ; 
and  2  catcher's  masks  at  $2.75  each.  Show  that  the  bill  was  paid 
10  days  after  its  date,  and  indicate  its  receipt. 


PRACTICAL   MEASUREMENTS 


SURFACE    MEASURE 


I.   The  Builder's  Applications 

(a)  Lumber  Measure.     The   unit    of  lumber  measure   is  the 
Board  Foot,  a  board  1  foot  long,  1  foot  wide,  and  1  inch  thick. 


l'xVxV'  =  l  board  foot. 
2'xl'xr'  =  2  board  feet. 
3'xrxl"  =  3  board  feet. 


4' 


1  board  foot. 

2  board  feet. 

3  board  feet. 

In  each  case : 

The  area  of  one  surface  in  square  feet  multiplied  hy  the  thickness 
in  inches  equals  the  number  of  hoard  feet  in  the  piece. 

i2«-     Length       4  ft. 
,5»  ''     Width         U  ft. 

Thickness  2  in.   4'  Xli'  X2"  =  10  board  feet. 

Length       6  ft. 
Width         f  ft. 
^"        Thickness  8  in.      6'  Xl'  X8"  =36  board  feet. 
Length       9  ft. 
l8"       Width        i  ft. 
3"         Thickness  8  in.  9' Xi'X8"  =  18  board 
feet. 

Lumber  less  than  1  inch  in  thickness  is  measured  as  if  it  were 
1  inch  thick. 

Lumber  more  than  1  inch  in  thickness  is  measured  by  its  actual 

thickness. 

Lumber  is  usually  bought  and  sold  by  the  thousand  board  feet, 
and  the  Roman  numeral  "  M  "  is  used  for  thousand. 

"  $36  per  M"  means  $36  per  one  thousand  board  feet. 
"  $36  per  M"  is  the  same  as  $.036  per  board  foot. 

13 


14  PRACTICAL  MEASUREMENTS 

BLACKBOARD    PRACTICE 

Find  the  number  of  board  feet  in  each  of  the  following  pieces, 
the  thickness  in  each  case  being  1  inch : 

1.  12'X12''.  9.  10'X8''. 

2.  14'X12^  10.  10' X3". 

3.  12'X10''.  11.  12'X3". 

4.  14'X10''.  •      12.  12' X4''. 
6.  12'X9".  13.  12'X6". 

6.  14'X10".  14.    14' X3", 

7.  12' X8".  15.    14' X6". 

8.  14' X9".  16.    14' X8". 

Find  the  number  of  board  feet  in  each  of  the  following,  the  length, 
the  width,  and  the  thickness  being  respectively : 


17. 

8'X15". 

18. 

8'X16". 

19. 

8'X15". 

20. 

10'X15". 

21. 

10'X16". 

22. 

10'X18". 

23. 

12'X15". 

24. 

12'X18". 

25. 

10'X12"X2". 

29. 

12'XlO"Xli". 

33. 

14'X6"X2". 

26. 

10'Xl2"xli". 

30. 

12'X10"X2". 

34. 

14'X6"X3". 

27. 

10'Xl2^'x2i". 

31. 

12'X8"X2|". 

35. 

14'X4"X2". 

28. 

12'X12"X3". 

32. 

12'X8"X3". 

36. 

14'x6"x2i". 

Find  the  number  of  board  feet  in  : 

37.  10  planks,  each  10  ft.  long,  10  in.  wide,  and  2  in.  thick. 

38.  12  planks,  each  14  ft.  long,  10  in.  wide,  and  2^  in.  thick. 

39.  20  planks,  each  12  ft.  long,  10  in.  wide,  and  2^  in.  thick. 

40.  16  planks,  each  12  ft.  long,  6  in.  wide,  and  4  in.  thick. 

41.  28  planks,  each  14  ft.  long,  2  in.  wide,  and  4  in.  thick. 

42.  40  boards,  each  12  ft.  long,  10  in.  wide,  and  |  in.  thick. 

43.  60  boards,  each  12  ft.  long,  12  in.  wide,  and  H  in.  thick. 

44.  Find,  to  the  nearest  cent,  the  cost  of  the  following  bill  of 
lumber  at  $30  per  M.  8  sills,  10"  X 12"  X 16',  12  posts,  6"X6"X20', 
2  beams,  8"X6"X12',  24  joists,  2"X8"X10'. 


LUMBER 


15 


45.  Find,  to  the  nearest  cent,  the  cost  of  the  following  bill  of 
lumber  at  $32.50  per  M.  10  sills,  10' X 12"  X 14",  4  beams,  6"X 
8"X12',  48  joists,  3"X8"X12',  120  boards,  rxi2"Xl2'. 

46.  In  1890  a  builder  could  buy  No.  1  spruce  lumber  at  $18 
per  M.  At  the  present  time  the  same  lumber  costs  $40  per  M. 
If  he  uses  spruce  lumber,  how  much  more  will  a  builder  pay  now 
than  in  1890  for  the  lumber  bill  in  example  45  ? 

(6)  Flooring.  Most  of  the  lumber  used  for  flooring  is  what 
is  known  as  ^'  matched  lumber,"  the  tongue  on  the  edge  of  one 
board  fitting  tightly  into  the  groove 
on  the  edge  of  the  next  board.  The 
loss  in  area  due  to  matching  is  usually 
made  up  by  increasing  the  estimate  of 
the  amount  of  surface  to  be  covered. 
For  flooring,  3  inches  or  less,  this  in- 
crease is  -^ ;  and  for  wider  flooring,  i. 


TONGUE 


GROOVE 


Illustrations : 

1.  How  many  feet  of  flooring  will  be  needed  for  a  room  16'  by 
12'  if  the  width  of  the  flooring  is  2^  inches? 

The  area  of  the  floor  =  (16  X 12)  sq.  ft.  =  192  sq.  ft. 
Allowing  for  an  increase  of  one  fourth  in  the  area  because  of  the  narrow 
flooring  used  : 

192  sq.  ft.+iof  192  sq.  ft.  =  (192+48)  sq.  ft.  =240sq.  ft. 

Therefore,  the  number  of  square  feet  of  flooring  required  =240.    Result. 

2.  At  $65  per  M,  how  much  will  4"  flooring  cost  for  a  rooro 
15' by  12'? 

The  area  of  the  floor  =  (15  Xl2)  sq.  ft.  =180  sq.  ft. 
Allowing  for  an  increase  of  one  fifth  in  the  area  because  of  the  wide 
flooring  used  : 

180  sq.  ft.+iof  180  sq.  ft.  =  (180+36)  sq.  ft.  =216sq.  ft. 
To  find  the  cost :  216  sq.  ft.  =  .216  M  board  feet. 

Then  .216 XS65  =$14.04,  the  cost.     Result. 


16 


PRACTICAL  MEASUREMENTS 


BLACKBOARD    PRACTICE 

Find  the  number  of  feet  of  2^"  flooring  needed  for  a  room : 

1.  14'X12'.  4.    15' X 12' 6''.  7.    12' 6"  X 10' 4". 

2.  15'X12'.  5.    16' X 12' 8".  8.    16' 4"  X 12' 6". 

3.  16'X16'.  6.    16' X 14' 6".  9.    16' 8"  X 14' 9". 

Find  the  cost  of  4"  flooring  at  $60  per  M  for  a  room : 

10.  15'X12'.  13.    12'6"X9'.  16.    12' 6" X 10' 6". 

11.  16'X14'.  14.    14' 8"  X 12'.  17.    14' 8"  X 12' 4". 

12.  18'X10'.  15.    16' X 14' 4".  18.    16' 6"  X 15' 3". 

(c)  Roofing.  The  unit  of  measure  for  roofing  is  the  square,  or 
100  square  feet.  The  materials  in  common  use  for  roofing  are 
wood  shingles  and  roofing  slate. 

Wood  shingles  average  16  inches  in  length  and  4  inches  in  width. 
Roofing  slate  is  cut  uniformly  16  inches  in  length  and  10  inches 
in  width. 


Both  are  laid  in  such  a  manner  as  to  overlap  and  completely 
cover  the  roof,  and  the  amount  of  exposed  surface  of  the  shingle 
or  slate  determines  the  number  that  will  be  required.  An  ex- 
posed length  of  4"  is  called  ''  4  inches  to  the  weather." 

If  shingles  are  laid  with 

4"  exposed,  1  shingle  covers  16  sq.  in.,  or  i  sq.  ft.,  and  900  cover  1 
square. 

4^"  exposed.  1  shingle  covers  18  sq.  in.,  or  ^  sq.  ft.,  and  800  cover  I 
square.  ' 


ROOFING  17 

If  slates  are  laid  with 

4"  exposed,  1  slate  covers  40  sq.  in.,  or  ^^  sq.  ft.,  and  360  cover  1  square. 
4^"  exposed,  1  slate  covers  45  sq.  in.,  or  y^g  sq.  ft.,  and  320  cover  1 
square. 

In  allowing  for  the  waste  in  shingles  it  is  customar^^  to  figure 
1000  to  a  square. 
No  allowance  for  waste  is  made  in  using  slate. 

Shingles  are  sold  in  bunches  of  250  each,  or  4  bunches  per 
thousand. 

Slates  are  sold  by  the  square. 

Roofing  Tin  is  usually  sold  in  sheets  20''  by  28'',  in  boxes  con- 
taining 112  sheets. 

In  laying  a  tin  roof  the  sheets  of  tin  overlap  at  the  seams.  A 
box  of  112  sheets  is  usually  estimated  to  cover  360  square  feet. 

BLACKBOARD    PRACTICE 

Making  no  allowance  for  waste,  and  laying  the  shingles  4"  to 
the  weather,  find  the  number  of  bunches  of  shingles  necessary  for 
both  sides  of  a  gable  roof  the  length  and  the  rafter  of  which  are 
respectively : 

1.  30',  12'.  4.   42',  15'  6".  7.    35'  8",  12'  6". 

2.  32',  14'.  5.   42',  16'  8".  8.   40'  8",  15'  9". 

3.  35',  16'.  6.   45',  14'  6".  9.    60'  6",  18'  6". 

If  shingles  cost  S4  per  thousand,  and  slate  $5.50  per  square, 
find  the  difference  in  the  cost  between  these  two  materials  for  the 
three  roofs  whose  length  and  rafter  are  given  below ;  both  ma- 
terials to  be  laid  4^"  to  the  weather,  and  no  allowance  to  be  made 
for  waste  on  the  shingles. 

10.    28',  12'.  11.    36'  6'^  16'  4".  12.   45'  6",  16'  6". 

13.  The  roof  in  the  figure  is  to  be  covered  with  1"  board- 
ing at   S30  per    M,  and  with  tin  at  50;^ 

$6.25  per  square.     Find  the  total  cost 
of  the  roof. 


18  PRACTICAL  MEASUREMENTS 

14.  A  contractor  estimates  the  cost  per  square  for  roofing 
the  building  at  the  left  as  follows : 

30' 

Roofing  tin $5.20 

Painting  two  coats 1.40 

lOJlHi         III  goidgj. 1_Q0 

Labor 2.25 

What  is  his  estimate  of  the  cost  of  the  roof? 

(d)  Lathing.  Laths  are  4  feet  long,  and  are  sold  in  bundles  of 
100.     A  bundle  will  usually  cover  6  square  yards. 

In  estimating  the  cost  of  lathing  a  room  the  openings,  that  is, 
the  area  of  all  doors  and  windows,  should  be  deducted. 

Illustrations : 

1.  How  many  bundles  of  laths  will  be  required  for  the  ceiling 
of  a  room  15'  long  and  12'  6"  wide? 

For  the  area  of  the  ceiling : 

(15X12.5)  sq.  ft.  =187.5  sq.  ft.  =21  sq.  yd. 

Since  one  bundle  covers  6  sq.  yd.,  21-r-6=32-  bundles. 

Half  bundles  are  not  sold,  hence  the  ceiling  requires  4  bundles.     Result. 

2.  How  many  bundles  of  laths  are  required  for  the  walls  and 
ceiling  of  a  room  15  ft.  long,  12  ft.  wide,  and  9  ft.  high,  allowing 
for  one  door  7  ft.  by  4  ft.,  and  two  windows,  each  6  ft.  6  in.  by  4  ft.  ? 

The  perimeter  of  the  room=2x  (15+12)  ft.=54  ft. 

Total  area  of  side  walls  (54x9)  sq.  ft.  =  486  sq.  ft. 

Area  of  ceiHng  (15  Xl2)  sq.  ft.  =  180  sq.  ft. 

Total  area  of  walls  and  ceiling  =  C66  sq.  ft. 

Area  of  door  (7  X4)  sq.  ft.  =                 28  sq.  ft.  ^ 

Area  of  windows  2  X  (6^  X4)  sq.  ft.  =  52  sq.  ft. 

Total  area  of  openings  =                        80  sq.  ft.  80  sq.  ft. 

Total  area  of  lathing  =  586  sq.  ft. 
586  sq.  ft.  =  (586 -^  9)  sq.  yd.  =65+  sq.  yd. 

The  estimate  should  cover  full  square  yards,  or  66  sq.  yd. 

Then:                  66  sq.  yd.-J-6  sq.  yd.  =  11  bundles.  Result. 


LATHING  19 

BLACKBOARD   PRACTICE 

1.  How  many  bundles  of  laths  will  be  needed  for  the  walls  of  a 
room  20'  X 14'  X  8'  if  an  allowance  of  100  sq.  ft.  is  made  for  openings? 

2.  If  the  laths  for  the  room  in  example  1  cost  S.45  per  bundle 
and  the  labor  cost  of  putting  them  on  is  $.25  per  bundle,  what  is 
the  cost  of  lathing  the  room? 

3.  A  room  is  18  ft.  long  and  14  ft.  wide.  There  are  three  doors, 
each  7  ft.  by  4  ft.,  and  two  windows,  each  6  ft.  by  4  ft.  If  the 
room  is  9  ft.  6  in.  high,  how  much  will  it  cost  to  lath  it  at  $.70  per 
bundle  including  labor? 

(e)  Plastering.  Plastering  is  usually  estimated  by  the  square 
yard.  On  new  work  plastering  and  lathing  are  usuall}'  figured 
together,  but  on  old  work  the  lathing  is  not  usually  included. 

The  methods  used  by  contractors  in  estimating  plastering  vary 
widely,  and  it  is  impossible  to  give  a  general  rule.  Contracts 
should  state  the  allowance  to  be  made  for  openings,  etc. 

In  the  illustration  below  and  in  obtaining  the  results  for  the  exercises 
that  follow,  a  fraction  of  a  square  yard  is  considered  a  square  yard ;  and 
full  allowance  is  made  for  openings. 

Illustration : 

A  room  is  24  ft.  long,  14  ft.  wide,  and  9  ft.  high.  There  are 
3  windows,  each  6  ft.  8  in.  by  4  ft.,  and  2  doorways,  each  7  ft.  4  in. 
by  4  ft.     Find  the  cost  of  plastering  the  room  at  $.35  per  sq.  yd. 

The  perimeter  of  the  room  =2 X (24  +  14)  ft.  =76  ft. 
Total  area  of  side  walls  =  (76  X9)  sq.  ft.  = 
Area  of  ceiling  =  (14  X24)  sq.  ft.  = 
Total  area  of  walls  and  ceiling  = 
Area  of  doors  =  2  X  (7i  X4)  sq.  ft.  = 

Area  of  windows  =  3  X  (6|-  X4)  sq.  ft.  = 

Total  area  of  openings  = 

Total  area  of  plastering  =  881  sq.  ft. 

881  sq.  ft.  =  (881-^9)  sq.  yd.  =98  sq.  yd.      (To  the  nearest  square  yard) 
Cost  of  plastering  =  98  X  $.35  =  $34.30.     Result, 


= 

684 

sq. 

ft. 

336 

_sqL 

ft. 

1020 

sq. 

ft. 

58| 

sq. 

ft. 

80 

sq. 

ft. 

138f 

sq. 

ft. 

or 

139 

sq. 

ft. 

20  PRACTICAL  MEASUREMENTS 

BLACKBOARD    PRACTICE 

Find  the  number  of  square  yards  in  a  ceiling  whose  dimensions 
are: 

1.  12'X12'.  7.    12'X10'6^  13.  10' 6'' X 12' 5". 

2.  14'X15'.  8.    15'X12'7".  14.  10' 8'' X 11' 6". 

3.  12'X16'.  9.    14' X 14' 8".  15.  12' 4"  X 14' 8". 

4.  14'X16'.  10.    15' X 18'  10".  16.  15' 9"  X 16'  6". 

5.  15'X17'.  11.    17'X21'6".  17.  18' 2" X 19' 4". 

6.  17'X18'.  12.    20' X  22' 4".  .     18.  20' 6"  X  24' 8". 

At  35^  per  square  yard  find  the  cost  of  plastering  a  room  whose 
dimensions  are : 

19.  10'X12'8"X8'.  24.  16' 6" X 18' 8" X 8' 6". 

20.  12'  4"X15'  6"X9'.  25.  18'  6"X20'  10"X9'  6". 

21.  12' 6"X16'8"X8'.  26.  20' 8" X 22' 8" X 9' 6". 

22.  13'8"X14'9"X9'.  27.  22' 4" X 24' 8" X 10' 6". 

23.  14'  10"  X 15' 9"  X 9'.  28.  24' 6"  X 28' 9"  X 10' 8". 

29.  A  room  is  14  feet  long,  10  feet  wide,  and  9  feet  high.  The 
total  area  of  the  openings  is  76  square  feet.  What  will  it  cost  to 
plaster  this  room  at  30^  per  square  yard? 

30.  A  room  24  feet  long  and  16  feet  wide  has  two  windows  each 
6  feet  by  3  feet  6  inches,  and  two  doors  each  7  feet  by  3  feet  6 
inches.  The  room  is  9  feet  8  inches  high.  At  35^  a  square  yard, 
what  will  it  cost  to  plaster  the  room? 

31.  A  room  25  feet  square  and  10  feet  high  has  one  door  7  feet 
by  8  feet,  one  door  7  feet  4  inches  by  3  feet  6  inches,  one  window 
4  feet  6  inches  by  6  feet,  and  two  windows  each  6  feet  by  3  feet. 
At  32^  a  square  yard,  what  will  it  cost  to  plaster  the  room? 

(/)  Painting.     Painting  is  usually  estimated  by  the  square  yard. 

No  general  rule  for  measurement  and  allowance  for  openings 
can  be  given,  for  local  customs  vary  considerably.  Your  local 
contractor  will  give  you  accurate  information  as  to  his  methods. 

1  gallon  of  paint  will  cover  250  square  feet  two  coats. 


PAINTING  21 

In  the  following  exercises  no  allowance  is  made  for  openings, 
because  the  labor  of  painting  around  doors  and  windows  and 
painting  window  sashes  is  as  great,  if  not  greater,  than  the  labor 
would  be  if  there  were  no  openings. 

BLACKBOARD   PRACTICE 

Allowing  250  sq.  ft.  of  surface  for  each  gallon  of  paint,  find  the 
number  of  gallons  necessary  for  painting  a  floor  whose  dimensions 
are : 

1.  12'X15'.  4.    16'X20'.  7.    20'X32'. 

2.  14'X16'.  5.    18'X22'.  8.   30'X45'. 

3.  15'X18'.  6.    19'X23'.  9.   35'X60'. 

At  20^  per  square  yard  for  two  coats  of  paint,  what  will  it  cost 
to  paint  the  walls  of  a  room  whose  dimensions  are : 

10.  128' X 14',  9' high?  13.    24' X 30',  12' high? 

11.  16' X 20',  9' high?  14.    35' X 60',  14' high? 

12.  18'X24',  10'  high?  15.   45'X80',  18'  high? 

At  10^  per  square  yard  find  the  cost  of  painting,  with  cold  water 
paint,  a  shop  whose  length  and  breadth,  and  height,  respectively, 
are : 

16.  40',  25',  and  10'.  19.    60',  35',  and  12'. 

17.  45',  30',  and  10'.  20.    90',  25',  and  14'. 

18.  50',  30',  and  12'.  21.    120',  40',  and  16'. 

One  gallon  of  varnish  covers  500  sq.  ft.  At  $3.00  per  gallon, 
find  the  cost  of  the  varnish  for  varnishing  a  floor : 

22.  12'X15'.  25.    15'X18'.  28.    18'X22'. 

23.  14'X16'.  26.    15'X20'.  29.    18'X25'. 

24.  14'X18'.  27.    16'X20'.  SO.    22'X24'. 

With  paint  costing  $1.60  a  gallon,  and  estimating  the  cost  of 
the  labor  to  be  three  times  the  cost  of  the  paint,  find  the  cost  of 


22  PRACTICAL  MEASUREMENTS 

painting  both  sides  of  a  fence  two  coats,  whose  length  and  height 
respectively  are : 

31.  75'  and  6'.  33.    100'  and  5'.  35.    250'  and  5'  8". 

32.  90'  and  5'.  34.    120'  and  6'.  36.    750'  and  6'  6". 

37.  Estimate  the  cost  of  painting  the  ceiling  of  your  school- 
room with  cold  water  paint  at  $.10  per  square  yard. 

38.  Find  the  cost  of  painting  the  barn 
shown  in  the  figure,  if  the  roof  is  painted  at 
a  cost  of  15(^  per  square  yard,  and  the  sides 
and  ends  at  20<f:  per  square  yard.  The  barn 
is  40'  long,  24'  wide,  12'  high  at  the  corners,  and  21'  high  at  the 
peak,  and  the  rafters  are  17'  long. 

39.  A  barn  is  80  feet  long,  35  feet  wide,  20  feet  high  at  the  eaves, 
and  15  feet  high  from  the  level  of  the  eaves  to  the  peak  of  the  roof, 
and  the  rafter  is  24  feet.  Find  the  cost  of  painting  the  barn,  in- 
cluding the  roof,  at  20  cents  a  square  yard. 

II.  The  Householder's  Applications 

(a)  Papering.     Wall  paper  is  sold   in  rolls,   and   a  standard 
single  roll  is  a  piece  8  yards  long  and  18  inches  wide. 
A  roll  is  often  spoken  of  as  a  piece. 

Paper  is  usually  shipped  from  the  factory  in  double  rolls,  that  is,  two 
single  rolls  in  one  long  strip^  The  plain  "felt"  papers  are  made  30  inches 
wide,  and  many  imported  papers  vary  from  the  standards  of  width  that 
have  been  adopted  by  domestic  manufacturers.  Borders  and  ornamental 
decorations  are  sold  by  the  yard.  In  contracts  for  wall  papering  there  is 
a  charge  for  the  paper  and  a  charge  for  hanging  it  on  the  wall.  The  cost 
of  hanging  varies  with  the  quality  of  the  paper. 

Because  of  the  loss  in  matching  patterns  it  is  impossible  to  estimate 
exactly  the  amount  of  paper  a  room  will  require.  Several  different 
methods  of  estimating  are  widely  used,  and  among  them  is  the  follow- 
ing. This  method  makes  a  liberal  allowance  for  matching  and  for  the 
deduction  for  openings, 


PAPERING  23 

Measure  the  perimeter  of  the  room  in  yards,  deducting  total  width 
of  openings. 

Allow  two  strips  of  paper  to  each  yard  in  this  result. 

Measure  the  height  of  the  room  and  determine  how  many  strips 
can  be  cut  from  a  single  roll. 

Divide  the  number  of  strips  required  by  the  number  you  can  cut 
from  a  single  roll. 

The  quotient  is  the  number  of  single  rolls  required. 

Illustration : 

1.  Find  the  number  of  rolls  of  paper  required  for  the  walls  of  a 
room  17'  by  13',  and  9'  high,  making  allowance  for  two  doors  and 
three  windows,  each  4'  wide. 

Perimeter  of  room  =2(17  +  13)  ft.  =2X30  ft.  =60  ft. 
Subtracting  width  of  openings,  60  ft.  —5  X4  ft.  =40  ft. 
40  ft.  changed  to  the  nearest  number  of  yards  =  14  yd. 
Number  of  strips  required  =2 X 14  =28  strips. 

Divide  length  of  roll  (24  ft.)  by  height  of  room  (9  ft.)  and  we  find  that 
2^  strips  per  roll  is  a  safe  estimate.     (Or  5  strips  per  double  roll.) 

Ti,en,  gumber  strips  needed  ^  28  ^  ^2,  the  number  of  rolls.     Result. 
Number  strips  per  roll      2^ 

BLACKBOARD    PRACTICE 

1.  How  many  rolls  of  paper  8  yards  long  and  18  inches  wide 
will  be  required  for  the  walls  of  a  room  14  feet  long  and  12  feet 
wide,  the  height  of  the  room  being  8  feet,  and  the  openings  one 
door  and  two  windows  each  4  feet  wide  ? 

2.  How  many  rolls  of  paper  30  inches  wide  will  be  needed  for 
the  walls  of  a  room  18  feet  square,  if  the  height  of  the  room  is 
9  feet,  and  the  allowance  for  openings  is  5  strips  ? 

3.  A  hall  is  32  feet  long,  and  14  feet  wide,  and  it  is  to  be  papered 
with  30-inch  felt  paper.  The  height  is  8  feet  6  inches,  and  the 
allowance  for  openings  includes  four  doors  each  4  feet  wide,  and 
one  door  6  feet  wide.  How  many  rolls  of  paper  will  be  needed 
for  the  walls  and  the  ceiling? 


24 


PRACTICAL  MEASUREMENTS 


4.  A  bedroom  14  feet  square  is  9  feet  high,  and  has  two  doors 
and  two  windows  each  4  feet  wide.  How  many  rolls  of  paper 
18  inches  wide  will  be  required  for  both  the  walls  and  the  ceiling? 
If  the  paper  costs  25^  per  roll  find  the  total  cost  of  the  paper. 

5.  Find  the  cost  of  papering  a  kitchen  14  feet  long,  10  feet 
wide,  and  9  feet  high ;  the  paper  costing  20^  per  roll,  the  cost  of 
hanging  it  being  $.15  per  roll,  and  the  allowance  for  openings 
being  one  fourth  the  total  area  of  the  side  walls.  Include  in 
your  estimate  the  cost  for  papering  the  side  walls  and  the  ceiling. 

6.  A  dining  room  18  feet  long,  14  feet  wide,  and  9  feet  high  has 
3  doors  and  3  windows,  each  4  feet  wide.  The  paper  used  for  the 
walls  cost  50i  per  roll  and  the  paper  used  for  the  ceiling  cost  25^ 
per  roll.  The  price  charged  for  hanging  the  paper  was  35^  per 
roll.     What  was  the  total  cost  of  papering  the  room? 

(6)  Carpeting.     Carpet  is  sold  by  the  linear  yard. 

The  better  grades  of  carpet  are  made  f  of  a  yard,  or  27  inches, 

wide,  and  the  cheaper  grades  are  made  1  yard  wide. 

With  plain  carpet  or  with  carpet  in  which  the  figures  are  small,  there 
is  no  loss  in  matching  patterns.  If  the  figure  is  large,  there  must  be  an 
allowance  on  each  strip  after  the  first  for  the  loss  in  matching  the  pattern. 


rs' 


18' 


16' 


16' 


If  the  strips  run  lengthwise : 

16  ft.  =  (16X12)  in. 

16X12      ^,     .  . 

=  71.  strips. 


If  the  strips  run  crosswise : 
18  ft.  =  (18X12)  in. 
18X12  ^gg^j.jpg^ 


27  '  9        -  27 

8  strips,  6  yards  long  —48  yd.  8  strips,  5^  yards  long  =42^  yd. 

With  carpet  at  $1  per  yard,  the  saving  in  the  second  ease  exceeds  $5.00. 
Floor  coverings  like  linoleum  and  matting  are  sold  by  the  linear  yard 
and  also  by  the  square  yard.     Most  linoleum  is  made  two  yards  wide. 


CARPETING  25 

BLACKBOARD   PRACTICE 

Find  the  number  of  yards  of  plain  carpet  1  yard  wide  required 
for  a  room  whose  dimensions  are : 

1.  12'X15'.                   4.    12'X16'.  7.    12' 6''X14' 6'^ 

2.  15'X18'.                   5.    15'X17'.  8.    15' 6'' X 18' 9". 

3.  12'X18'.                  6.    18'X20'.  9.    16' 8"X20' 6". 
Find  the  number  of  yards  of  plain  carpet  f  of  a  yard  wide  re- 
quired for  a  room  whose  dimensions  are : 

10.  12'X15'.  13.    12'X16'.  16.    15' X 12' 8". 

11.  15'X18'.  14.    15'X21'.  17.    16' X 20' 8". 

12.  12'X18'.                 15.    15'X24'.  18.    18' X 24' 6". 
With   plain  carpet  27  inches  wide  find  how  much  the  carpet 

will  cost  for  each  of  the  following  rooms,  the  dimensions  of  the 
room  and  the  price  per  yard  being  respectively : 

19.  14' X 16'  ($1.20  per  yard).       24.    16' X 28'  ($1.00  per  yard). 

20.  16' X 18'  ($1.00  per  yard).       25.    24' X 26'  ($1.90  per  yard). 

21.  15' X 17'  ($1.10  per  yard).       26.    24'X  15'  ($1.65  per  yard). 

22.  15' X 19'  ($1.30  per  yard).       27.    25' X 20'  ($1.75  per  yard). 

23.  18' X 12'  ($1.60  per  yard).       28.    27' X 22'  ($2.00  per  yard). 

29.  Find  the  cost  of  the  material  for  the  rug 
shown  in  the  figure,  the  material  being  f  yard  wide, 
and  the  allowance  for  waste  at  the  corners  being 
twice  this  width;  and  the  cost  of  the  material 
$1.20  per  yard. 

30.  A  room  15'  wide  h  carpeted  with  carpet  1  yard  wide.  The 
.strips  run  lengthwise  and  the  room  is  18'  long.  If  ^  of  a  yard  is 
lost  in  matching  each  strip  after  the  first  strip,  how  many  yards 
of  carpet  will  be  needed  ? 

31.  A  floor  is  to  be  covered  with  carpet  27"  wide,  and  the  loss 
in  matching  is  |^  of  a  yard  per  strip  after  the  first  strip.  The 
carpet  cost  $2.25  per  yard.  The  room  is  16  feet  long  and  15  feet 
wide.  Which  is  the  more  economical  way  to  run  the  strips,  and 
what  is  the  cost  of  the  carpet  ? 


26  PRACTICAL  MEASUREMENTS 

III.   The  Contractor's  Applications 

Paving.  Paving  estimates  are  based  upon  the  square  foot  or 
square  yard. 

While  the  contractor  gives  his  estimates  in  square  yards  of  the 
surface  of  the  finished  product,  his  own  problem  includes  the  ma- 
terial necessary  for  foundations  and  the  work  necessary  to  lay 
them. 

BLACKBOARD    PRACTICE 

At  14^  per  square  foot,  find  the  cost  of  building  a  concrete 
sidewalk : 

1.  100  feet  long,  4  feet  wide.  6.  800  feet  long,  5  feet  wide. 

2.  150  feet  long,  5  feet  'wide.  7.  50  yards  long,  3  feet  wide. 

3.  240  feet  long,  3|-  feet  wide.  8.  75  yards  long,  4^  feet  wide. 

4.  300  feet  long,  6  feet  wide.  9.  90  yards  long,  5  feet  wide. 

5.  500  feet  long,  4^  feet  wide.  10.  125  feet  long,  1  yard  wide, 

11.  200  yards  long,  5  feet  4  inches  wide. 

12.  350  feet  long,  8  feet  5  inches  wide. 

At  21^  per  square  foot,  find  the  cost  of  a  concrete  floor  for  a 
cellar : 

13.  35  feet  long,  25  feet  wide.       15.   40  feet  long,  32  feet  wide. 

14.  65  feet  long,  32  feet  wide.       16.   84  feet  long,  45  feet  wide. 
At  $2.40  per  square  yard,  find  the  cost  of  an  asphalt  paving 

for  a  street : 

17.  100  feet  long,  40  feet  wide.  21.  175  yards  long,  60  feet  wide. 

18.  150  feet  long,  32  feet  wide.  22.  450  feet  long,  75  feet  wide. 

19.  250  feet  long,  50  feet  wide.  23.  1000  feet  long,  50  feet  wide. 

20.  100  yards  long,  50  feet  wide.  24.  1500  feet  long,  60  feet  wide. 

25.  One  half  mile  long,  60  feet  wide. 

26.  Two  miles  long,  50  feet  wide. 

27.  For  a  rectangular  court  100' X 60'. 

28.  For  a  square  court  108  feet  on  each  side. 


PAVING 


27 


If  brick  cost  $32.00  per  thousand  laid,  and  each  brick  has  a 
surface  of  9''X3'',  find  the  cost  of  paving  a  street : 

29.  100  feet  long,  45  feet  wide.     32.    500  feet  long,  60  feet  wide. 

30.  150  feet  long,  48  feet  wide.     33.    1200  feet  long,  50  feet  wide. 

31.  200  feet  long,  60  feet  wide.     34.    1  mile  long,  75  feet  wide. 
At  $0.90  per  square  yard  find  the  cost  of  a  macadam  road : 

35.  2  miles  long,  16  feet  wide.       38.    5  miles  long,  16  feet  wide. 

36.  1^  miles  long,  20  feet  wide.     39.   8  miles  long,  18  feet  wide. 

37.  4  miles  long,  18  feet  wide.      40.    10  miles  long,  16  feet  wide. 

41.  The  courtyard  of  an  apartment  house  is  42  ft.  3  in.  long 
and  31  ft.  9  in.  wide.  Find  the  cost  of  paving  this  court  with 
concrete  at  $1.44  per  square  yard. 

42.  The  floor  of  a  manual  training  room  is  36  ft.  long  and  24  ft 
wide,  and  the  cost  of  paving  it  with  concrete  was  SI 68.     Hot/ 
much  did  the  paving  cost  per  square  j^ard? 

43.  The  figure  at  the  right  represents 
a  grass-plot  surrounded  by  a  concrete 
walk.  How  many  square  yards  are  there 
in  the  surface  of  the  walk  if  it  is  3  ft. 
wide? 


24  yd 


44.  The  figure  at  the  right  represents 
a  courtyard,  with  concrete  walks  as  indi- 
cated, each  5  ft.  wide.  How  many  square 
yards  are  there  in  the  walks  ? 

45.  A  houseowner  builds  a  concrete 
walk  on  the  two  sides  of  his  corner  prop- 
erty. With  the  dimensions  as  in  the 
figure,  how  much  does  the  walk  cost 
him  at  $.24  per  square  foot? 


• 

16  yd 

1 

1 

1 

J_     .   .1..    J.  i.-.. 

1 

1 

1 

135' 

75'  5' 
160' 

:.               ) 

75' 


28 


PRACTICAL  MEASUREMENTS 


VOLUME  MEASURE 

I.   The  Farmer's  Applications 

(a)  Wood  Measure.     The    unit    of    measure   for   firewood   is 
the  Cord. 

A  cord  of  wood  is  8  feet  long,  4  feet  high,  and  4  feet  wid-^. 


The  length  of  the  sticks,  4  feet,  is  a  standard  length.  When 
wood  is  cut  in  lengths  shorter  than  4  feet,  a  pile  8  feet  long  and 
4  feet  high  is  often  considered  a  cord ;  and  the  price  is  determined 
by  the  length  of  the  sticks. 

BLACKBOARD  PRACTICE 

Find  the  number  of  cords  of  4-foot  wood  in  a  pile : 

1.  16'X4'.  4.    16'X5'.  7.   30'X4'.         10.   62'X5'. 

2.  12'X4'.  5.    12'X6'.  8.    36'X5'.  11.   80'X4'. 

3.  24^X4'.  6.   24'X5'.  9.   40'X6'.  12.    72'X8'. 

Find  the  number  of  cords  of  16-inch,  or  stove-wood,  in  a  pile : 

13.  12'X4'.  16.    18'X5'.  19.    36'X4'.         22.   80'X5'. 

14.  16' X4'.  17.    20' X 5'.         20.   40' X 5'.         23.    100' X 6'. 

15.  18'X6'.         18.    24'X6'.         21.   48'X6'.         24.    120'X4'. 


CAPACITY  OF  BINS 


29 


25.  A  load  of  wood  measures  5  feet  long,  4  feet  wide,  and  3  feet 
high.    How  much  must  I  pay  for  six  such  loads  at  $4.50  per  cord? 

26.  A  wagon-box  is  filled  with  4-foot  wood.  The  inside  of  the 
box  is  8  feet  long,  4  feet  wide,  and  3  feet  deep.  How  many  cords 
can  be  delivered  by  this  wagon  in  seven  loads  * 

(5)  Capacity  of  Bins.  While  wheat,  corn,  £nd  other  grains  are 
usually  sold  by  weight,  the  farmer  has  frequent  need  for  estimat- 
ing the  quantity  of  grain  in  his  bins  without  actually  weighing  it. 
For  this  purpose  he  makes  use  of  the  approximate  relations  be- 
tween such  units  as  the  bushel  and  the  cubic  foot,  and  he  has 
frequent  need  for  the  following : 


Approximate  Equivalents 
1  bushel  shelled  grain  =  1^  cu.  ft. 
1  bushel  com  on  the  ear  =  1^  cu.  tt. 
1  ton  well-settled  hay  =  450  cu.  ft. 


It  will  be  helpful  to  remember  that : 

1.  The  capacity  of  a  bin  in  bushels 

=  4  of  the  number  of  cubic  feet  in  its  volume. 

2.  The  number  of  cubic  feet  for  a  given  number  of  bushels 

=  -|-  of  the  number  of  bushels  given. 


BLACKBOARD    PRACTICE 

Find  the  number  of  bushels  of  shelled  grain  that  can  be  placed 
in  a  bin  whose  dimensions  are 

5'6''X8'X4'. 

6'6''X4'6''X3'. 

8'8''X3'6''X4'4". 

10'8''X6'8"X5'4^ 

12'8''X6'8''X5'4''. 

16'  6"X10'4"XS'  6''. 


1. 

4'X3'X3'. 

7 

2. 

8'X5'X3'. 

8 

3. 

10'X4'X4'. 

9 

4. 

12'X6'X5'. 

10 

5. 

15'X8'X9'. 

11 

6. 

18' X 12' X 10'. 

12 

30 


PRACTICAL  MEASUREMENTS 


Find  the  number  of  cubic  feet  of  space  that  must  be  provided 


for  a  quantity  of  grain  amounting  to : 

13.  250  bu.  16.    520  bu.         19.  1000  bu. 

14.  300  bu.  17.    650  bu.         20.  1250  bu. 

15.  450  bu.  1«.    900  bu.         21.  1500  bu. 


22.  2500  bu. 

23.  3000  bu. 

24.  7200  bu. 


1.  24' X  18^X8'. 

2.  25'X20'X8'. 

3.  28'X20'X9'. 

4.  30'X25'X9'. 


45'X25'6"X8'6''. 
48'X24'8"X9'6''. 
50'X25'6"X9'6". 
64'6''X48'6"X9'. 


II.  The  Contractor's  Applications 

(a)  Excavations.     The  cost  of  cellars,  ditches,  wells,  etc.,  is 
estimated  by  the  cubic  yard. 

BLACELBOARD   PRACTICE 

Find  the  cost,  at  $.45  per  cubic  yard,  of  excavating  a  cellar 
whose  dimensions  are : 

5.  30'X27'X8'.  9. 

6  38'X27'X8' 6".  10. 

7.  40'X30'X9'  6".  11. 

8.  45'X32'X19'.  12. 

Find  the  cost,  at  $.45  per  cubic  yard,  of  digging  a  ditch  : 

13.  45'  long,  5'  deep,  2'  wide.      15.   65'  long,  6'  deep,  2'  wide. 

14.  48'  long,  4'  deep,  2'  wide.      16.   75'  long,  4'  deep,  3'  wide. 

17.  2  miles  long,  4'  deep,  1'  6"  wide. 

18.  3  miles  long,  4'  8"  deep,  1'  6"  wide. 

19.  What  is  the  cost  of  a  mile  of  ditch 
li  feet  wide  and  3  feet  deep  at  $.40  per 
cubic  yard  ? 

20.  With  the  dimension  shown  in  the 
figure  at  the  right,  find  the  cost  of  digging 
the  cellar  at  $.45  per  cubic  yard. 

21.  A  contractor  digs  a  cellar  with  di- 
mensions as  in  the  figure  at  the  right,  and 
he  receives  $.35  per  cubic  yard  for  the 
work.     How  much  does  he  receive? 


BRICKWORK  31 

(6)  Brickwork.  The  number  of  bricks  required  for  a  wall  is 
estimated  by  the  thousand. 

As  a  rule,  a  cubic  foot  of  wall  laid  in  mortar  requires  22  bricks 
of  the  ordinary  size.     This  size  is  8"  long,  4''  wide,  and  2"  thick. 

In  estimating  the  cost  of  labor  in  bricklajdng  it  is  common  practice 
to  measure  the  outside  of  the  walls,  which  really 
results  in  counting  each  corner  twice.  As  the  con- 
struction of  a  corner  makes  additional  work,  this 
practice  is  considered  fair  to  both  the  workman  and 
the  builder.  And  no  allowance  is  made  for  openings, 
because  the  openings  add  greatly  to  the  labor  re- 
quired. 

In  estimating  the  amount  of  material  in  brick- 
work the  corners  are  counted   only  once,  and  some 

allowance  is  made  for  the  openings.  There  is  some  variation  in  the 
methods  used  in  different  localities,  and  your  own  local  contractors  will 
give  you  the  method  they  use. 

Illustrations : 

1.  Find  the  number  of  bricks  required  for  a  wall  36  feet  long, 

14  feet  high,  and  1  foot  thick,  allowing  22  bricks  to  the  cubic 

foot.     Find  the  cost  of  labor  at  $8.25  per  thousand. 

For  the  number  of  bricks  :  36X14X1X22=  11.088  M. 
For  the  labor  :  11.088x$8.2o  =  $91.48. 

2.  Find  the  number  of  bricks  and  the  cost  of  the  labor  at  $7.90 
per  thousand  for  a  foundation  wall  of  a  house  28'  by  20',  the  walls 
to  be  8'  high  and  1'  thick. 

Outside  measure  of  wall  =  perimeter  =  2X  (28+20)  ft.  =  96  ft. 
For  the  number  of  bricks  :  96  X8  X 1  X22  =  16.896  M. 
For  the  labor :  16.896  X$7.90  =  $133.48. 

To  estimate  the  number  of  brick  needed  for  a  wall  we  maj^  use 
the  following  rules : 

If  the  wall  is  to  be  1  brick  thick,  multiply  the  area  of  the  wall 
in  square  feet  by  7 ;  if  the  wall  is  to  be  2  bricks  thick,  multiply 
the  area  of  the  wall  by  14 ;  if  it  is  to  be  3  bricks  thick,  multiply 
the  area  of  the  wall  by  21,  etc. 


32  PRACTICAL  MEASUREMENTS 

BLACKBOARD   PRACTICE 

Find  the  number  of  bricks  required  for  a  wall  with  the  following 
dimensions,  using  22  bricks  per  cubic  foot : 

1.  30'  long,  12'  high,  1'  thick. 

2.  35'  long,  10'  high,  1   thick. 

3.  40'  long,  9'  high,  18"  thick. 

4.  45'  long,  12'  high,  15"  thick. 

5.  50'  long,  16'  high,  1'  thick. 

6.  75'  long,  6'  high,  1'  thick. 

7.  100'  long,  4'  high,  1'  thick. 

8.  120'  long,  5'  high,  15"  thick. 

9.  200'  long,  4'  high,  1'  thick. 
10.  200'  long,  4^'  high,  U'  thick. 

If  bricks  are  laid  on  edge,  and  if  six  bricks  are  allowed  to  every 
square  foot  of  surface,  find  the  number  of  bricks  necessary  for  a 
driveway : 

11.  60'  long,  7'  wide.  15.  125'  long,  8'  wide. 

12.  75'  long,  8'  wide.  16.  130'  long,  9'  wide. 

13.  90'  long,  6'  6"  wide.  17.  145'  long,  10'  wide. 

14.  100'  long,  7'  wide.  18.  150'  long,  10'  6"  wide. 

19.  The  rear  wall  of  a  storage  house  is  40'  wide,  34'  high,  and 
8"  thick.     Find  the  number  of  bricks  necessary  to  build  the  wall. 

20.  How  many  bricks  are  needed  for  a  wall  3  ft.  high,  240  ft. 
long,  and  2  bricks  thick? 

21.  A  floor  is  supported  through  the  center  by  four  brick  piers, 
each  12  feet  high  and  2  feet  square.  The  bricks  cost  $7.75  per 
thousand,  and  the  mortar  and  labor  together  cost  $8.50  per  thou- 
sand.    Find  the  total  cost  of  the  four  piers. 


CONCRETE  33 

(c)  Concrete.  Concrete  walls  and  foundations  are  estimated 
by  the  cubic  yard. 

In  concrete  work  the  labor  of  making  the  "  forms,"  the  wooden 
frames  into  which  the  wet  concrete  is  poured,  is  estimated  and 
included  by  the  contractor  in  his  price.  Corners  are  counted 
but  once,  and  as  a  rule  an  allowance  is  made  for  the  openings. 
The  variations  in  the  price  of  concrete  work  are  due  to  the  char- 
acter of  the  mixture,  some  concrete  being  much  richer  in  cement 
than  others,  and  some  being  mixed  with  crushed  stone  instead 
of  the  cheaper  cinders  or  sand  and  gravel. 

Illustration : 

The  concrete  foundation  walls  for  an  assembly  hall  100  feet 
long  and  50  feet  wide  are  8  feet  high  and  1  foot  6  inches  thick. 
The  corners  are  counted  only  once,  and  there  are  ten  openings 
each  4  feet  long  and  2  feet  deep.  Find  the  total  cost  of  the  con- 
crete walls  at  $7.50  per  cubic  yard. 

Counting  the  corners  only  once,  the  total  length  of  the  finished  wall  is 
2(100+50)  ft.  -4(thickness  of  wall  in  feet)  =300  ft.  -6  ft.  =294  ft. 
Volume  of  waU  (294X8X1.5)  cu.  ft.  =3528  eu.  ft. 
Deducting  openings :    10   openings  each   4  ft.  long,  2  ft.   deep,  and 
1  ft.  6  in.  thick  : 

10X4X2X1.5  cu.  ft.  =120cu.  ft. 
Changing  to  cubic  yards,  3408  cu.  ft.  =  126f  cu.  yd. 
For  the  cost:  126fX $7.50  =$946.67.     Result. 

BLACKBOARD   PRACTICE 

Counting  the  corners  but  once  and  making  no  allowance  for 
openings,  at  $7.50  per  cubic  yard  find  the  cost  of  18-inch  founda- 
tion walls  for  a  building  : 

1.  30  feet  long,  18  feet  wide,  8  feet  high. 

2.  36  feet  long,  20  feet  wide,  9  feet  high. 

3.  40  feet  long,  24  feet  wide,  8  feet  high. 

4.  60  feet  long,  32  feet  wide,  9  feet  high. 

5.  Find  the  cost  of  a  concrete  wall  150  feet  long,  6  feet  high, 
and  10  inches  thick,  at  $8.25  per  cubic  yard. 


34  PRACTICAL  MEASUREMENTS 

6.  Find  the  cost  of  a  concrete  wall  200  ft.  long,  3  ft.  high,  and 
1  ft.  wide,  at  $9.25  per  cubic  yard. 

7.  Find  the  cost  of  24  concrete  posts,  each  6  ft.  long,  and  1  ft. 
square,  at  $.72  a  cubic  foot. 

8.  Find  the  cost  of  a  concrete  pillar  12  ft.  high,  2  ft.  wide,  and 
1  ft.  thick,  at  $16.75  per  cubic  yard. 

9.  100  concrete  fence  posts  were  each  7  ft.  long,  and  6  inches 
square.     At  $.45  a  cubic  foot,  how  much  did  the  posts  cost? 

10.  A  wall  is  240  ft.  long,  5  ft.  high,  2  ft.  wide  at  the  bottom, 
and  1  ft.  wide  at  the  top.  Using  the  "  average  thickness  "  of 
the  wall,  how  many  cubic  yards  of  concrete  are  there  in  it? 

11.  The  figure  at  the  right  represents 
a  foundation  wall  for  a  house.  The 
wall  is  15  inches  thick,  and  costs  $8 
per  cubic  yard.  No  allowance  being 
made  for  openings,  find  the  total  cost 
of  the  wall. 

12.  In  concrete  work  a  1:2:4  mixture  is  a  mixture  made  of 
1  part  cement,  2  parts  sand,  and  4  parts  crushed  stone.  If  a 
contractor  uses  this  mixture  for  a  wall  containing  1400  cubic 
feet,  how  much  cement,  how  much  sand,  and  how  much  crushed 
stone  does  he  use? 

13.  A  contractor  builds  a  wall  for  a  house  48  feet  long  and  28 
feet  wide,  the  wall  being  8  feet  high  and  18  inches  thick.  He 
makes  no  allowance  for  openings,  and  uses  a  1:2:4  mixture. 
At  $1.30  per  bag,  what  does  the  cement  cost  him,  a  bag  of  cement 
being  equal  to  1  cubic  foot? 

(d)  Stonework.     Stonework  is  estimated  by  the  Perch,  or  by 
the  cubic  foot,  or  by  the  cubic  yard. 
A  Perch  is  a  volume  of  24"^  cu.  ft. 


STONEWORK  35 

This  unit  is  based  upon  a  volume  16J  ft.  by  1^  ft.  by  1  ft.= 
24f  cu.  ft. 

For  convenience  in  figuring,  a  perch  is  often  estimated  at 
25  cubic  feet. 

The  labor  for  stonework  is  estimated  exactly  as  it  is  for  brickwork,  the 
corners  are  counted  twice,  and  no  allowance  is  made  for  openings. 

Material  for  stonework  is  estimated  exactly  as  it  is  for  brickwork,  the 
corners  are  counted  only  once,  and  an  allowance  is  made  for  the  openings, 

BLACKBOARD  PRACTICE 

Find,  to  the  nearest  perch,  the  stonework  in  a  wall : 

1.  40  ft.  long,  5  ft.  high,  and  1  ft.  thick. 

2.  75  ft.  long,  6  ft.  high,  and  1  ft.  6  in.  thick. 

3.  100  ft.  long,  4  ft.  6  in.  high,  and  1  ft.  8  in.  thick. 

4.  225  ft.  long,  5  ft.  6  in.  high,  and  1  ft.  4  in.  thick. 

5.  240  ft.  long,  3  ft.  8  in.  high,  and  1  ft.  3  in.  thick. 

6.  400  ft.  long,  4  ft.  4  in.  high,  and  1  ft.  6  in.  thick. 

Find,  to  the  nearest  perch,  the  stonework  in  a  24-inch  founda- 
tion wall : 

7.  8  ft.  high,  for  a  house  32  ft.  by  24  ft. 

8.  9  ft.  high,  for  a  house  45  ft.  by  24  ft.  6  in. 

9.  8  ft.  6  in.  high,  for  a  house  45  ft.  by  32  ft. 

10.  9  ft.  6  in.  high,  for  a  house  65  ft.  6  in.  long  by  32  ft.  wide. 

11.  8  ft.  9  in.  high,  for  a  house  45  ft.  long  and  28  ft.  6  in.  wide. 

12.  9  ft.  9  in.  high,  for  a  house  54  ft.  6  in.  long  and  24  ft.  8  in. 
wide. 

13.  Find  the  number  of  perches  of  stonework  in  a  foundation 
wall  represented  by  the  figure  at  the  right, 
the  walls  being  1  ft.  thick. 

14.  If  the  mason  received  $1.90  per 
perch  for  the  labor,  what  was  the  cost  of 
the  labor  for  the  foundation  wall  repre- 
sented by  the  figure  at  the  right  ? 


SAVING   AND   INVESTING   MONEY 
UNITED   STATES   GOVERNMENT  WAR-SAVINGS  CERTIFICATES 

The  War-Savings  Plan  was  established  by  the  United  States 
Government  to  encourage  habits  of  saving,  and  to  provide  money 
for  increased  government  expenses.  Under  the  plan  Thrift 
Stamps  are  sold  for  twenty-five  cents  each,  and  with  the  first 
purchase  a  Thrift  Card  is  given  to  the  investor.  When  filled  the 
Thrift  Card  holds  sixteen  Thrift  Stamps,  and  represents  a  saving 
of  four  dollars.  Thrift  Stamps  do  not  earn  interest,  but  the 
War-Savings  Stamps  for  which  they  are  exchanged  bear  interest 
until  the  Government  pays  the  loan  four  years  later.  Thus,  the 
series  of  War-Savings  Stamps  which  was  sold  in  1918  will  be  paid 
by  the  Government  on  January  1,  1923,  and  the  series  sold  in 
1919  will  be  paid  on  January  1,  1924. 

A  War-Savings  Stamp  is  purchased  with  a  filled  Thrift  Card,  or 
with  cash ;  and  costs  the  investor  four  dollars  plus  a  small  num- 
ber of  cents  as  indicated  in  the  table : 

Cost  of  War-Savings  Stamps  in  the  Year  19 19 


January 

$4.12 

May 

$4.16 

September 

$4.20 

February 

4.13 

June 

4.17 

October 

4.21 

March 

4.14 

July 

4.18 

November 

4.22 

April 

4.15 

August 

4.19 

December 

4.23 

The  stamps  of  this  series  will  be  worth  $5.00  on  January  1,  1924. 

A  War-Savings  Certificate  contains  spaces  for  twenty  stamps, 
and,  when  filled,  represents  the  saving  of  eighty  dollars,  increased 
by  the  total  of  the  cents  paid  for  the  stamps  in  the  months  in 
which  they  were  purchased.  An  investor  may  buy  a  quantity 
of  War-Savings  Stamps  at  one  time,  without  using  the  Thrift 
Cards ;  but  no  investor  may  hold  more  than  two  hundred  War- 
Savings  Stamps  of  a  single  issue. 

36 


WAR-SAVINGS  PLAN  37 

Investment  Value  of  War-Savings  Stamps  and  Certificates 

Suppose  you  buy  in  the  month  of  November,  1919,  enough  War-Savings 
Stamps  to  fill  a  War-Savings  Certificate. 

Your  twenty  stamps  will  cost  20  XS4.22  =$84.40. 

On  January  1,  1924,  the  Government  will  pay  you  $100  for  your  Cer- 
tificate. 

Therefore,  the  profit  on  your  investment  will  be 

$100.00  -$84.40  =$15.60. 
WRITTEN   APPLICATIONS 

1.  Find  the  cost  of  5  War-Savings  Stamps  bought  in  June. 
1919. 

2.  Find  the  cost  of  24  War-Savings  Stamps  bought  in  July 
1919. 

3.  Find  the  cost  of  20  War-Savings  Stamps  bought  in  Sep- 
tember, 1919. 

4.  Find  the  cost  of  75  War-Savings  Stamps  bought  in  Novem- 
ber, 1919. 

5.  Find  the  profit  that  will  be  made  on  20  War-Savings  Stamps 
bought  in  Jaiy,  1919,  if  the  investor  holds  them  until  January  1, 
1924. 

6.  How  much  profit  will  an  investor  make  if  he  buys  20  W^ar- 
Savings  Stamps  in  August,  1919,  20  more  in  October,  1919,  and 
20  more  in  December,  1919,  and  holds  them  all  until  January  1, 
1924? 

7.  A  boy  saved  $1  each  week  for  15  weeks,  and  then  $2  each 
week  for  24  weeks.  If  he  bought  War-Savings  Stamps  with  this 
money,  purchasing  them  all  in  September,  1919,  how  much  did 
he  pay  for  them?  How  much  profit  will  he  make  on  them,  if  he 
holds  them  until  January  1,  1924? 


THE  SOLUTION  OF  PROBLEMS   BY  ANALYSIS 

I.    ORAL   ANALYSIS 

In  solving  a  problem  we  may  use  two  different  methods,  and 
by  either  method  arrive  at  the  same  result. 

Indirect  Analysis.     Illustration : 

50  books  cost  a  dealer  $100.  How  much  will  75  books  cost  at  the 
same  price  per  book? 

In  working  indirectly,  we  first  find  the  cost  of  one  book. 

If  50  books  cost  $100,  1  book  costs  $100  divided  by  50,  or  $2. 

If  1  book  costs  $2,  75  books  will  cost  75  times  $2,  or  $150.     Result. 

This  method  is  often  called  Unitary  Analysis,  for  in  using  it  we  seek  for 
information  concerning  a  single  article. 

Direct  Analysis.    Illustration : 

50  books  cost  a  dealer  $100.  How  much  will  75  books  cost  at  the  same 
price  per  book? 

In  working  directly  we  begin  with  the  number  asked  for  by  the  ques- 
tion. 

How  is  75  related  to  50  ?     75  is  ^^  or  ^  of  50. 

50  books  cost  $100 ;  therefore,  75  books  will  cost  3  of  $100,  or  $150. 
Result. 

This  method  is  often  called  Comparison,  for  in  using  it  we  compare  the 
given  number  and  the  required  number  and  obtain  thereby  a  relation  be- 
tween a  given  result  and  the  required  result. 

Method  and  Accuracy.  If  you  were  required  to  find  the  cost 
of  91  books  in  the  above  illustration,  you  would  have  to  use  the 
indirect  analysis.  Use  your  judgment  in  selecting  the  method 
best  suited  to  a  problem.  But  remember,  always,  that  Accu- 
racy is  absolutely  essential,  and  that  a  result  is  either  exactly 
right  or  wholly  wrong. 

Estimating  the  Answer.  Practical  business  men  frequently 
make  a  rough  estimate  of  an  answer  before  making  a  careful  solu- 
tion. Unreasonable  answers  are  avoided  if  an  estimate  of  a  result 
is  made  in  advance. 

38 


ORAL  ANALYSIS  39 

ORAL    PRACTICE 

(The  following  exercises  should  be  solved  indirectly) 

1.  If  5  pencils  cost  25  cents,  how  much  will  8  pencils  cost  ? 

2.  If  7  oranges  cost  28  cents,  how  much  will  10  oranges  cost  ? 

3.  If  4  coats  cost  $12,  how  much  will  9  coats  cost? 

4.  If  9  books  cost  $18,  how  much  will  13  books  cost? 

5.  If  8  barrels  of  flour  cost  $48,  how  much  will  5  barrels  cost? 

6.  If  7  tons  of  coal  cost  $35,  how  much  w411  4  tons  cost? 

7.  How  much  will  8  bushels  of  oats  cost  if  11  bushels  cost  $6? 

8.  $180  were  paid  for  4  cows.     How  much  will  7  cows  cost  at 
the  same  rate? 

9.  9  pigs  were  sold  for  $54.     At  the  same  rate  how  much  wdll 
13  pigs  sell  for? 

10.  How  much  will  15  chickens  cost  if  9  chickens  cost  $4.50? 

11.  If  1  pound  of  coffee  costs  30^,  how  many  pounds  can  be 
bought  for  $1.50? 

12.  What  is  the  cost  of  12  lemons  when  they  are  selling  at  5 
for  10  cents? 

13.  How  much  must  I  pay  for  15  towels  when  they  are  selling 
at  4  for  $1? 

14.  How  many  dozen  eggs  can  be  bought  for  $1.75  if  $1  will 
buy  4  dozen  ? 

15.  If  a  bus  runs  4  blocks  in  5  minutes,  how  many  blocks  can 
it  run  in  30  minutes  ? 

(The  following  exercises  should  be  solved  directly) 

16.  If  6  pounds  of  tea  cost  $3,  how  much  will  12  pounds  cost? 

17.  If  9  pencils  cost  27  cents,  how  much  will  3  pencils  cost? 

18.  If  16  cards  cost  80  cents,  how  much  w^ill  8  cards  cost? 

19.  If  12  bottles  of  ink  cost  60  cents,  how  many  bottles  can  be 
bought  for  40  cents  ? 

20.  If  18  pounds  of  butter  is  sold  for  $5.40,  for  what  amount 
will  27  pounds  sell? 


40  ANALYSIS 

21.  How  much  must  I  pay  for  18  tablets,  if  12  tablets  are  sold 
for  $.96? 

22.  If  oranges  are  selling  at  3  for  10  cents,  how  much  will  30 
oranges  cost? 

23.  If  oranges  are  selling  at  4  for  15  cents,  how  much  will 
4  dozen  oranges  cost? 

24.  If  an  automobile  runs  45  miles  in  3  hours,  how  far  will  it 
run  in  6  hours? 

25.  How  much  must  I  pay  for  6  oranges,  if  they  are  selling  at 
4  for  10  cents  ? 

26.  What  is  the  cost  of  7  pounds  of  butter,  if  14  pounds  cost 
$3.00? 

27.  If  a  wheel  turns  18  times  in  10  seconds,  how  many  turns 
will  it  make  in  1  minute  ? 

28.  If  a  watch  loses  1  minute  in  36  hours,  how  much  does  it 
lose  in  6  days? 

29.  If  100  lb.  of  meat  cost  $18,  how  much  will  75  lb.  cost? 

30.  If  a  trolley  car  runs  4  miles  in  30  minutes,  how  far  does  it 
run  in  3  hours? 

(Select  the  better  method  for  solving  the  following  exercises) 

31.  A  boy  bought  5  pencils  at  3  cents  each  and  had  10  cents 
left.     How  much  money  did  he  have  before  he  bought  the  pencils? 

32.  A  boy  earned  $1  and  with  it  bought  2  books  at  35^  each. 
How  much  of  it  had  he  left  ? 

33.  A  girl  gave  a  merchant  a  2-dollar  bill  in  payment  for 
3  hair  ribbons  costing  40^  each.  How  much  should  she  receive 
in  change? 

34.  A  grocer  bought  25  pounds  of  butter  at  30^  per  pound, 
and  sold  it  for  34^  per  pound.     How  much  did  he  make  on  the  . 
transaction  ? 

35.  A  boy  spent  $1.25  for  feed  for  his  chickens,  and  sold  5  dozen 
eggs  at  40^  per  dozen.  How  much  more  did  the  eggs  bring  than 
the  feed  cost? 


ORAL  ANALYSIS  41 

36.  Working  Saturdays  in  a  store  a  boy  earned  50^  on  each  of 
28  days.  He  bought  a  coat  from  his  employer  for  $9.  How 
much  was  then  due  him  in  cash? 

37.  A  man  earned  $1000  in  one  year,  and  spent  $750  for  his 
board,  clothing,  and  general  expenses.  If  he  saved  the  balance, 
what  fraction  of  his  earnings  did  he  save? 

38.  A  man  spent  f  of  his  income  on  his  board,  clothing,  and 
general  expenses,  and  saved  the  balance  which  was  $250.  How 
much  did  he  spend? 

39.  Two  thirds  of  a  man's  money  amounts  to  $4000,  and  is 
invested  in  Liberty  Bonds.  If  the  balance  is  in  the  bank,  how 
much  has  he  in  the  bank? 

40.  A  watch  gains  ^  of  a  minute  in  3  days.  At  this  rate  how 
many  minutes  will  it  gain  in  30  days  ? 

41.  If  1^  pounds  of  meat  cost  a  housekeeper  $.25,  what  was  the 
cost  of  the  meat  per  pound? 

42.  A  man  bought  a  lot  for  $2000,  and  on  the  lot  he  built  a 
house  costing  $6000.  What  part  of  the  cost  of  the  house  is  the 
cost  of  the  lot  ? 

43.  In  the  preceding  problem  find  what  part  of  the  total  cost 
of  the  house  and  the  lot  is  represented  by  the  cost  of  the  lot ;  by 
the  cost  of  the  house. 

44.  One  third  of  a  man's  property  is  left  to  his  family,  and  the 
family  receives  $40,000.  What  is  the  total  amount  of  the  properjty 
he  left  ? 

45.  Two  fifths  of  the  value  of  a  farm  is  invested  in  the  build- 
ings, which  cost  the  owner  $3000.  What  is  the  total  value  of 
the  land  and  the  buildings? 

46.  A  builder  paid  $12  per  thousand  for  15,000  brick,  and  one 
half  the  cost  of  the  brick  for  a  concrete  foundation.  What  was 
the  total  cost  of  the  brick  and  the  concrete  foundation  ? 

47.  30  men  can  dig  a  trench  for  a  sewer  m  5  days.  In  how  many 
days  can  10  men  dig  this  trench? 


42  ANALYSIS 

48.  10  men  can  dig  a  field  of  potatoes  in  4  days.  In  how  many 
days  can  5  men  dig  the  same  field  of  potatoes  ? 

49.  It  took  5  men  3  hours  to  load  a  car  with  lumber.  On  the 
following  day  2  men  load  a  similar  car  with  lumber.  How  long 
does  it  take  them? 

60.  3  men  work  8  hours  a  day  to  paint  a  house  in  5  days.  4 
men  are  working  10  hours  a  day  to  paint  the  same  kind  of  house. 
In  how  many  days  should  the  second  house  be  painted? 

II.   WRITTEN   ANALYSIS 

The  Problems  of  Everyday  Life  in  business  and  in  the  home 
are  mainly  of  a  simple  character,  and  a  great  majority  of  them 
require  nothing  beyond  an  intelligent  use  of  arithmetic  through 
fractions  and  common  measures. 

Accuracy  is  the  first  essential  in  all  arithmetical  processes. 

Systematic  Arrangement  is  one  of  the  greatest  aids  to  accuracy. 

The  student  should  learn  at  the  outset : 

1.  To  be  accurate. 

2.  To  be  sj^stematic. 

3.  To  test  every  result  by  checking. 

Business  men  do  not  forget  or  forgive  errors,  —  they  replace 
inaccurate  clerks  with  those  who  are  accurate  and  careful.  Speed 
is  desirable  if  it  is  not  obtained  at  a  sacrifice  of  accuracy,  but 
a  person's  accuracy  and  not  his  speed  determine  his  real  worth 
in  a  business  house. 

Checking  is  the  practice  of  testing  each  step  of  the  work  after 
it  is  completed.  In  engineering,  every  process  and  calculation 
is  checked  by  another  person  or  persons  after  the  engineer  or 
draftsman  has  made  the  original  calculations,  and  a  careful  record 
is  kept  of  the  individuals  who  have  taken  part  in  every  problem. 
Careless  and  inaccurate  assistants  are  speedily  dismissed,  since 
errors  might  cause  the  loss  of  thousands  of  dollars  or  hundreds 
of  lives. 


WRITTEN  ANALYSIS  43 

Systematic  Method.     In  the  following  exercises : 

1.  Read  the  problem  carefully. 

2.  Estimate  the  answer  in  advance  when  it  can  he  done. 

3.  Make  a  careful,  systematic  solution. 

4.  Check  every  step  in  tJie  process  and  in  the  calculations. 

WRITTEN   APPLICATIONS 

I.   The  Business  Man's  Use  of  Analysis 

1.  60  overcoats  are  bought  for  $8  each,  and  are  sold  at  a  gain 
of  $2.50  each.     How  much  is  received  for  all  of  the  coats? 

2.  A  bag  of  salt  containing  100  pounds  costs  a  grocer  $.75. 
How  much  does  he  gain  by  selling  the  salt  in  10-pound  bags  at 
12  cents  each? 

3.  From  a  bolt  of  bunting  containing  48  yards,  a  dealer  sold 
16  yards.     What  fractional  part  of  the  whole  bolt  did  he  sell  ? 

4.  If  a  merchant  buys  dress  goods  at  $1.20  per  yard  and  sells 
it  at  $1.45  a  yard,  how  many  yards  must  he  sell  to  gain  a  profit 
of  $10? 

5.  10  dozen  eggs  are  bought  by  a  country  grocer  for  $.55 
per  dozen.  How  many  yards  of  cloth  at  $.06^  per  ysLrcl  should 
he  give  in  pajmient  for  the  eggs? 

6.  A  coal  dealer  bought  50  tons  of  coal  at  the  mine  for  $4.25 
per  ton.  The  freight  being  $.42  per  ton,  how  much  did  the  coal 
cost  him  at  his  yard? 

7.  A  dry  goods  merchant  sold  f  of  a  yard  of  silk  for  $2.25. 
At  the  same  rate,  how  much  should  he  charge  for  2^  yards  of  the 
silk? 

8.  A  piano  dealer  offers  to  sell  a  piano  for  $400  cash,  or  for 
$450  in  installments.  What  fractional  part  of  the  cash  price 
does  he  add  to  the  price  if  he  is  paid  in  installments? 

9.  A  dealer  in  sewing  machines  received  24  payments  of  $1.25 
each  for  a  machine.  His  profit  on  this  machine  was  $10.  How 
much  did  the  machine  cost  him  ? 


44  ANALYSIS 

10.  A  shoe  dealer  sold  45  pairs  of  slippers  at  f  of  the  regular 
price.     If  he  received  $45  for  them,  what  was  the  regular  price? 

11.  A  merchant's  profits  for  the  year  amount  to  $2160,  and  this 
amount  exceeds  by  i  his  profits  for  the  preceding  year.  How 
much  were  his  profits  during  the  preceding  year  ? 

12.  From  a  ham  weighing  16|  pounds,  a  butcher  sold  2^  pounds 
to  one  woman  and  half  as  much  to  another.  How  many  pounds 
of  this  ham  were  left  ? 

13.  An  insurance  firm  charges  6^  per  $100  for  liability  insurance 
on  a  certain  risk.  How  much  do  they  charge  for  such  insurance 
amounting  to  $12,500? 

14.  Three  sales  of  5^  yards,  8  yards,  and  12f  yards,  respectively, 
were  made  from  a  bolt  containing  40  yards  of  cloth.  How  much 
is  the  rest  of  it  worth  at  24^  per  yard? 

15.  A  dealer  bought  a  box  containing  40  dozen  lemons  for  $6 
and  then  sold  them  at  25^  a  dozen.  How  much  did  he  make 
on  them? 

16.  A  dealer  in  gasoline  used  a  5-gallon  can  in  emptying  a 
tank,  and  he  filled  the  can  38  times.  How  much  was  the  gasoline 
worth  at  14^  per  gallon? 

17.  A  firm  paid  $10.76  for  a  barrel  of  flour  weighing  193  pounds, 
and  sold  it  all  in  8  equal  sacks  at  8^  per  pound.  Find  the  price 
of  each  sack  and  also  the  gain  on  all  of  it. 

18.  25  cases  of  a  cereal,  containing  2  dozen  packages  to  the 
case,  cost  $1  a  dozen.  ^  of  the  cereal  spoiled,  and  the  rest  was 
sold  at  15^  per  box.  Did  the  grocer  gain  or  lose,  and  how 
much? 

19.  A  coal  company  bought  600  long  tons  of  coal,  2240  pounds 
to  the  ton,  at  $4  per  ton ;  and  sold  it  all  by  the  short  ton  of  2000 
pounds,  receiving  $4.50  per  ton  for  it.  What  was  the  profit  on 
this  transaction? 

20.  Two  men  together  own  -f^  oi  a  motorboat,  and  one  of  theni 
owns  3  times  as  large  a  share  as  the  other.  What  fraction  of  the 
value  of  the  boat  does  each  man  own? 


WRITTEN  ANALYSIS  45 

II.   The  Housekeeper's  Use  of  Analysis 

21.  A  lady  paid  $1.00  for  f  of  a  yard  of  silk.  What  was  the 
cost  of  the  silk  per  yard  ? 

22.  A  woman  exchanged  10  yards  of  cloth  worth  45^  a  yard  for 
handkerchiefs  worth  $2.25  per  dozen.  How  many  handkerchiefs 
should  she  receive? 

23.  A  butcher  charged  48cf  for  a  slice  of  ham  weighing  1^  pounds. 
How  much  is  this  per  pound  ? 

24.  A  woman  exchanged  8  dozen  eggs  worth  55^  a  dozen  for 
granulated  sugar  worth  9^^  a  pound.  How  many  pounds  of  sugar 
should  she  receive? 

25.  A  housekeeper  found  that  8  tons  of  coal  at  $5  per  ton 
supplied  her  range  for  one  year.  How  much  did  the  coal  cost  to 
supply  the  range  one  week? 

26.  A  woman  finds  that  her  stair  carpet  must  cover  15  stairs, 
and  she  allows  f  yd.  for  each  stair.  How  much  does  the  carpet 
cost  at  $1.75  per  yard? 

27.  In  canning  fruit  a  woman  uses  24  pounds  of  sugar,  which 
is  one  half  of  the  weight  of  the  fruit  used.  How  much  does  the 
fruit  cost  at  8^  per  pound? 

28.  If  the  sugar  used  in  problem  27  cost  9^^  per  pound  and 
the  fruit  filled  40  cans,  find  the  total  cost  of  each  can. 

29.  A  housewife  bought  a  sewing  machine,  paying  $1  per  week 
for  28  weeks.  The  cash  price  was  $23.50.  How  much  could  she 
have  saved  by  paying  cash  ? 

30.  In  a  month  of  30  days  a  family  used  2  quarts  of  milk  and 
9^  worth  of  cream  daily.  What  is  their  expense  for  milk  and 
cream,  if  the  milk  costs  14^  a  quart? 

31.  A  wife  has  $16  a  week  with  which  to  pay  her  maid  and  buy 
groceries,  meat,  and  milk,  i  of  this  amount  goes  to  her  maid, 
$7.25  for  groceries,  and  the  rest  for  meat  and  milk.  How  much 
is  paid  for  these  last  two  items? 


46  ANALYSIS 

32.  A  dealer  sold  a  housekeeper  4^  dozen  eggs  at  30^  a  dozen, 
^  bushel  of  potatoes  at  $.80  a  bushel,  and  ^  peck  of  apples  at  30^ 
a  peck.  How  much  change  should  he  give  her  from  a  two-dollar 
bill  ? 

33.  A  widow  spends  ^  of  her  annual  income  for  rent,  $25  a 
month  for  food,  and  $50  a  year  for  clothing.  The  balance,  $160, 
she  saves  each  year.     Find  the  amount  of  her  annual  income. 

34.  A  woman  finds  that  she  can  rent  an  apartment  for  $24 
per  month,  including  the  heat,  or  that  she  can  rent  a  small  house 
for  $18  per  month  which  will  require  9  tons  of  coal  at  $7  per  ton 
during  the  year.  Which  is  the  cheaper  plan  for  her  to  follow  if 
no  charge  is  made  for  caring  for  the  heater  ? 

35.  A  housekeeper  owning  her  house  rents  two  rooms  for  $2.25 
a  week  each,  two  others  at  $2  a  week,  and  a  fifth  at  $1.75  a  week. 
Her  annual  expenses  for  running  the  house  are :  Taxes,  $65.40 ; 
interest,  $54  ;  repairs,  $20  ;  and  heat  and  light,  $100.  How  much 
profit  does  she  make  in  one  year  by  renting  these  rooms  ? 

III.   The  Farmer's  Use  of  Analysis 

36.  A  quart  of  milk  weighs  about  2.2  pounds.  How  many 
quarts  are  there  in  125  pounds  of  milk? 

37.  A  farmer  sold  11  head  of  cattle,  which  was  5  more  than  ^ 
of  his  whole  herd.     How  many  cows  were  there  in  his  herd? 

38.  A  farmer  finds  that  f  of  an  acre  produces  90  bushels  of 
potatoes.     At  that  rate  how  many  bushels  do  6  acres  produce? 

39.  I  of  a  pasture  was  sold  to  a  farmer,  and  the  man  who  sold 
it  to  him  retained  10  acres  of  it  for  his  own  use.  How  many  acres 
were  there  in  the  original  pasture? 

40.  f  of  a  crop  of  grain  was  sold  for  $50,  and  the  50  bushels 
remaining  unsold  brought  $30  later  in  the  season.  What  prices 
were  received  per  bushel  at  each  sale? 

41.  A  real  estate  operator  offers  a  farmer  $2000  for  i  of  his  land, 
and  $60  an  acre  for  the  remaining  80  acres.  What  is  the  total  offer 
for  all  of  the  land  ?     What  is  the  offer  per  acre  for  ^  of  the  land  ? 


WRITTEN  ANALYSIS  47 

42.  A  farmer  requires  some  ''1-2-4"  concrete;  that  is,  1 
part  cement,  2  parts  sand,  and  4  parts  gravel.  If  he  uses  1  barrel 
of  cement  and  2  barrels  of  sand,  how  many  barrels  of  gravel  should 
he  use? 

43.  If  he  requires  700  cubic  feet  of  concrete,  how  many  cubic 
feet  of  each  ingredient  will  he  use?  (A  ''  1-2-4  "  mixture  has 
1  part  +  2  parts  +  4  parts,  or  7  parts  in  all.) 

44.  A  farm  laborer  earns  $1.25  a  day  besides  his  board,  and  his 
average  daily  expense  for  clothing,  etc.,  is  $.50.  He  already  has 
$55  and  wishes  to  save  enough  to  make  it  $100.  In  how  many 
days  should  he  save  the  desired  amount  ? 

45.  A  farmer  has  720  bushels  of  wheat,  and  two  thirds  of  the 
number  of  bushels  of  wheat  he  has  is  equal  to  three  fourths  of  the 
number  of  bushels  of  corn  that  he  must  buy.  How  much  will 
this  corn  cost  him  at  $.60  per  bushel? 

46.  A  farmer  offers  to  exchange  a  quantity  of  wheat  for  a 
mowing  machine  costing  $45.50,  a  rake  costing  $32.00,  and  a 
wagon  costing  $87.00.  If  his  wheat  is  worth  $1.75  a  bushel,  how 
many  bushels  must  he  give  in  exchange  for  these  implements? 

47.  The  foundation  for  a  silo  requires  280  cubic  feet  of  con- 
crete, and  the  1-2-4  mixture  is  used.  Find  the  amount  of  cement, 
sand,  and  gravel  needed  to  build  the  foundation. 

48.  A  farmer  raises  a  crop  of  110  barrels  of  fancy  appies  for 
which  he  is  offered  $2.50  a  barrel  He  declines  the  offer  and 
buys  enough  half -peck  baskets  at  3^  each,  in  which  to  pack  the 
entire  crop,  each  barrel  containing  2^  bushels.  He  retails  these 
baskets  of  apples  at  $.20  each.  Allowing  for  the  cost  of  the 
baskets,  how  much  more  did  he  receive  by  retailing  his  apples? 

.  49.  A  farmer  uses  a  2-ton  truck  for  delivering  2400  bushels  of 
potatoes,  and  averages  2  tons  to  the  load  on  each  trip.  If  the 
truck  uses,  on  the  average,  a  gallon  of  gasoline  to  every  8  miles, 
and  if  the  distance  traveled  on  each  round  trip  is  5  miles,  find  the 
cost  of  delivering  the  potatoes ;  the  gasoline  costing  22^  a  gallon, 
and  the  labor  $.75  each  trip. 


THE   EQUATION 

Statement  of  Equality.     When  we  make  a  statement  that  a 
number  of  units  of  one  kind  is  equal  to  a  number  of  units  of  another 
kind  we  make  a  statement  of  equality. 
For  example : 

"  Ten  dimes  are  equal  to  one  hundred  cents." 
"  Thirty-two  ounces  are  equal  to  two  pounds." 

Finding  the  Value  of  a  Unit.  From  a  statement  of  equality 
like  those  illustrated  above;  we  find  the  value  of  a  single  unit  or 
thing  by  division. 

For  example : 

We  know  that  10  dimes  are  equal  to  100  cents. 

Expressing  the  words  "  are  equal  to  "  by  the  familiar  sign  of 
equality,  "  =," 

We  may  write  10  dimes  =  100  cents. 

Dividing  by  10,  1  dime  =  10  cents 

An  Equation  is  a  statement  of  equality  between  two  quantities 
or  between  two  numbers. 

Using  a  Letter  in  an  Equation.  Suppose  we  make  the  state- 
ment that  five  wagons  cost  three  hundred  dollars.  With  the 
symbols  that  we  have  long  used,  we  write  briefly 

5  wagons  cost  $300. 

Suppose  we  use  the  first  letter  "  w  "  of  the  word  "  wagons  "  and 
since  cost  means  "  cost  an  amount  equal  to  "  use  the  sign  '*  =  " 
for  the  word  "  cost." 

We  have  then,  5w  =  %S00. 

Dividing  each  by  5,  1  w;  =  |60. 

These  two  ''  equations  "  are  the  briefest  possible  form  of  ex- 
pression for  the  statement  in  analysis  that  '^  If  5  wagons  cost  $300, 
1  wagon  will  cost  i  of  $300,  or  $60." 

Applying  the  same  principle  : 

If  4  0=20,  If  5  ^  =  60,  If  10  X  =70,  If  4  a;  =56, 

o=5.  6  =  12.  x=7,  ;  x  =  14. 

48 


THE  EQUATION  AND  THE  BALANCE 


49 


Comparison  of  an  Equation  and  a  Balance.  A  little  investiga- 
tion will  convince  you  that  the  members  of  an  equation  may  be 
compared  to  the  weights  on  the  pans  of  a  balance. 

Suppose  in  (a)  that  each  pan  of  the  bal- 
ance has  4  one-pound  weights.  Then,  the 
scales  exactly  balance 

And,  arithmetically,  4=4.  (a) 

Suppose  in  (6)  that  we  add  two  more  one- 
pound  weights  to  each  pan.  The  scales  are 
still  in  exact  balance. 

And,  arithmetically,  4=4. 

Adding,  2=2.  (b) 

Or,  6=6. 

Suppose  in  (c)  that  we  have  removed  two 
one-pound  weights  from  the  original  num- 
ber in  each  pan.  The  scales  are  still  in  exact 
balance. 

And,  arithmetically,  4=4.  {() 

Subtracting,  2=2. 

Gives  2=2. 

Clearly,  therefore, 

1.  If  equals  are  added  to  equals,  the  sums  are  equal. 

2.  If  equals  are  subtracted  from  equals,  the  remainders  are  equal. 

If  we  multiply  the  original  number  of  weights  in  each  pan  by  the  same 
number,  we  shall  have  the  same  number  in  each. 

That  is,  originally,  4  lb.  =4  lb. 

And  for  twice  as  many  weights  in  each,  2  X4  lb.  =2  X4  lb. 

Or,  81b.  =8  lb. 

Also,  if  we  divide  the  original  number  of  weights  in  each  pan  by  the 
same  number,  we  shall  continue  to  have  the  same  number  in  each. 

That  is,  originally,  4  lb.  =4  lb. 

And  for  half  as  many  weights  in  each,  4  lb.-^2  =4  lb.-^2. 

Or,  •  2  lb.  =2  lb. 

Clearly,  therefore, 

3.  If  equals  are  multiplied  by  equals,  the  products  are  equal. 

4.  If  equals  are  dinided  by  equals,  the  quotients  are  equal. 


50  THE  EQUATION 

Changing  a  Number  from  One  Member  of  an  Equation  to  the 
Other  Member. 

We  know  that  10+4  =  14.  (I) 

Subtracting  4  from  each  member, 

10+4-4  =  14-4. 
Simplifying,  since  4-4=0,  10  =  14-4.  (2) 

Observe  that  in  (1)  4  is  seen  in  the  first  member  with  a  +  sign,  and  in 
(2)  4  is  seen  in  the  right  member  with  a  —  sign. 

Therefore,  4  might  have  been  written  in  the  other  member  with  its 
sign  changed  from  +  to  — . 

Again,  take  10-4=6.  (1) 

Adding  4  to  each  member,     10-4+4  =  6+4. 

Simplifying,  since  4-4=0,  10  =  6+4.  (2) 

Here,  also,  —4  might  have  been  written  in  the  second  member  with 
its  sign  changed  from  —  to  +. 

Hence,  a  number  may  he  changed  from  one  member  of  an  equa- 
tion to  the  other  if  its  sign  is  changed  either  from  -\-  to  — ,  or  from 
-  to  +. 

Unknown  Numbers.  Each  of  the  following  equations  has  a 
letter  whose  value  is  unknown.  Finding  the  value  of  an  unknown 
letter  is  solving  an  equation. 

Hlustrations : 

1.  Solve  x+4  =  10. 

Change  +4  to  the  other  member  and  change  its  sign, 

a:=10-4. 
Subtracting,  x  =  6.         Result. 

2.  Solve  x-3=9. 

Change  +3  to  the  other  member  and  change  its  sign, 

a:  =9+3. 
Adding,  x  =  12.       Result. 


USING  LETTERS  TO  REPRESENT  QUANTITIES         51 

3.  Solve  2x+3  =  15. 

Change  +3  to  the  other  member  and  change  its  sign, 

2  X  =  15-3. 
Subtracting,  2  x  =  12. 

Dividing  by  2,  x=  6.     Result. 

4.  Solve  5x-2  =  l. 

Change  —2  to  the  other  member  and  change  its  sign, 

5a:  =  l+2. 
Adding,  5x=3. 

Dividing  by  5,  *  ^=f«     Result. 

BLACKBOARD   PRACTICE 

Solve  the  following  equations  : 

1.  x-\-5  =  9.       8.   x-3  =  8.     15.    5x  =  35.  22.    3x-l  =  14. 

2.  x+6  =  9.       9.   x-8  =  9.     16.    6x  =  3.  23.   4a:-3  =  13. 


3. 

a:+8  =  9. 

10. 

2x  =  10. 

17.   4x  =  7. 

24. 

6x+4  =  16 

4. 

a:+2  =  6. 

11. 

2x=16. 

18.    5x  =  ll. 

25. 

7x-3  =  19 

5. 

a:+4  =  8. 

12. 

3a:=15. 

19.    2x+3  =  9. 

26. 

ox+4  =  21 

6. 

x-l  =  9. 

13. 

4x  =  24. 

20.    3x+2  =  8. 

27 

8x+l  =  25 

7. 

0^  —  5  =  7. 

14. 

6a;=18. 

ORAL 

21.    5x+l  =  16. 
PRACTICE 

28. 

9x-2  =  30 

Using  Letters  to  Represent  Quantities 

1.  Numbers  of  the  same  kind  may  be  added.  Thus:  $10+$5 
=  $15;  10^+5(^=15^;  10  lb.+51  lb.=  ?  lb. ;  10  yd. +5  yd.  =  ?  yd. 

2.  Can  you  add  $5  and  3  yd.?  10  yd.+3  lb.?  8  rd.+5^? 
Wliy  is  it  that  you  cannot  add  in  such  cases? 

3.  Sometimes  we  indicate  a  sum  because  we  cannot  add  the 
forms  that  are  given.  Thus,  we  may  be  asked  for  the  sum  of 
10  ft. +6  in.  We  cannot  add,  however,  until  both  measures  are 
expressed  in  the  same  unit. 

4.  Read  these  indicated  sums.  5  yards+12  feet.  8  rods-f- 
5  yards+2  feet.     2  ton+3  hundredweight +75  pounds. 


52  THE  EQUATION 

5.  Can  you  see  that  each  of  the  expressions  in  problem  4  is 
merely  a  compound  denominate  number  with  the  plus  sign  be- 
tween the  denominations  ? 

6.  If  you  are  12  years  old  now,  how  old  will  you  be  in  5  years? 
12  years +5  years  may  be  written  in  the  form  (12+5)  years. 

7.  If  you  are  12  years  old  now,  how  old  will  you  be  in  x  years? 
12  years + a:  years  may  be  written  in  the  form  (12+ a:)  years.  Can 
you  do  any  more  than  merely  indicate  the  addition? 

8.  If  you  are  12  years  old  now,  how  old  will  you  be  in  y  years? 
How  old  will  you  be  in  z  years?  How  old  will  you  be  in  m-\-n 
years?     How  old  w^ll  you  be  in  n+p  years? 

9.  If  you  are  12  years  old  now,  how  old  were  you  5  years  ago  '^ 
12  years  — 5  years  =?  years.  12  years  less  5  years  may  be  ex- 
pressed in  the  form  (12  —  5)  years. 

10.  If  you  are  12  years  old  now,  how  old  were  you  y  years  ago? 
12  years  — 2/  years  may  be  expressed  {12  — y)  years.  Give  the 
expression  for  your  age  ^  years  ago. 

11.  Jack  has  25  cents  and  Edith  has  20  cents.  Both  have  the 
sum  of  25  cents  and  20  cents,  or  (25+20)  cents.  How  many 
cents  have  both  ?     How  many  more  cents  has  Jack  than  Edith  ? 

12.  Suppose  that  Jack  has  25  cents,  and  thc.t  Edith  iias  x  cents. 
We  may  express  the  number  of  cents  that  both  have  by  writing 
(25 +a:)  cents.  But  until  we  know  how  many  cents  are  repre- 
sented by  X  cents,  can  we  add  the  number  of  cents  that  both 
have  ? 

13.  Mary  solved  15  examples,  and  Jane  solved  twice  as  many. 
Therefore,  Jane  solved  2  times  15,  or  (2X15)  examples,  or  30 
examples.  (2X15)  is  an  indicated  multiplication,  but  we  can  do 
the  work  asked  for  and  get  what  number? 

14.  Suppose  we  were  told  that  Mary  solved  x  examples  and 
that  Jane  solved  twice  as  many.  Indicating  the  number  that 
Jane  solved,  we  write  (2  times  x)  examples.  This  can  be  written 
in  the  simpler  form  ''  2  x."  (We  mean  2  times  1  hat  when  we 
say  "  2  hats."     We  mean  2  times  1  x  when  we  say  or  write  ^*  2  x.") 


SOLVING  proble:\is  by  equations  53 

Using  an  Equation  in  Analysis.  In  solving  a  problem  by  using 
an  equation  you  should  observe  the  following  steps. 

1.  Read  the  problem  carefully  to  find  what  is  wanted. 

2.  Represent  the  unknown  number  by  x. 

3.  The  problem  will  give  a  statement  about  the  unknown  number. 
Write  that  statement,  using  x  for  that  unknown  number. 

4.  Solve  the  equation. 

>VRITTEN   APPLICATIONS 

I.   Given :    A  Product  and  One  of  Its  Factors. 

To  Find  :    The  Other  Factor. 

Illustration : 

Five  times  a  certain  number  is  35.     What  is  the  number  ? 

Let  a:  =  the  unknown  number. 

Then  5  x  =five  times  that  unknown  number. 

But  we  know  that  35  =five  times  that  unknown  number. 

Therefore,  5x=35. 

Hence,  x=7.     Result. 

1.   Seven  times  a  number  is  112.     What  is  the  number? 
2    Nine  times  a  number  is  144.     What  is  the  number? 

3.  What  number  multiplied  by  13,  gives  a  product  of  156? 

4.  $175  was  divided  among  7  children,  each  receiving  the  same 
amount.     How  many  dollars  did  each  receive? 

5.  1350  tons  of  coal  were  shipped  in  cars  holding  45  tons  each. 
How  many  cars  were  required  to  ship  this  coal? 

6.  Twelve  laborers  were  paid  $216  for  their  work  on  a  street 
improvement.  If  each  laborer  received  the  same  amount,  how 
much  did  each  laborer  receive? 

7.  A  mile  track  was  laid  out  in  16  sections  for  a  boys'  relay 
race.  If  the  sections  were  all  equal  how  many  feet  were  there  in 
each  section  ? 


54  THE  EQUATION 

II.   Given :    A  Sum  and  One  of  Its  Parts. 
To  Find  :    The  Other  Part. 

Illustration : 

What  number  increased  by  35  is  equal  to  90? 

Let  X  =  the  unknown  part. 

Then  x  +35  =  the  sum  of  both  parts. 

But  we  know  that        90  =  the  sum  of  both  parts. 
Therefore,  x+35=90. 

Hence,  x  =  90  —  35. 

Or,  a*  =55.     Result. 

8.  What  number  increased  by  25  equals  110? 

9.  What  number  increased  by  37  equals  145? 

10.  What  numl^er  decreased  by  21  equals  93? 

11.  What  number  decreased  by  34  equals  115? 

12.  A  boy  earns  45  cents,  and  then  has  88  cents.  How  much 
had  he  at  first  ? 

13.  A  boy  saved  98  cents  and  after  buying  some  school  supplies 
with  it  had  only  62  cents  of  it  left.  How  much  did  he  spend  for 
the  supplies? 

14.  A  thrifty  young  man  finds  that  by  saving  $150  more  he 
will  have  $1000.     How  much  has  he  at  the  present  time? 

15.  A  farmer's  daughter  canned  145  quarts  of  strawberries, 
and  kept  60  cans  for  home  use,  and  sold  the  rest.  How  many 
cans  did  she  sell? 

16.  A  man  is  34  years  older  than  his  boy,  and  the  sum  of  their 
ages  is  66  years.     How  old  is  the  boy  ? 

17.  John  and  his  father  together  weigh  235  pounds,  and  John 
weighs  90  pounds.     How  many  pounds  does  his  father  weigh  ? 

18.  Two  men  bought  a  boat  and  one  of  them  furnished  $24 
more  of  the  money  than  the  other.  If  the  boat  cost  $  136,  how 
much  did  each  man  furnish  ? 


SOLVING  PROBLEMS  BY  EQUATIONS  55 

ni.   Given :     The  Sum  of  Two  Numbers  and  Their  Relation 
to  Each  Other. 

To  Find  :    The  Numbers. 

Illustration : 

The  sum  of  two  numbers  is  45,  and  one  of  them  is  twice  the 
other.     What  are  the  numbers  ? 

Let  X  =  the  smaller  number. 

Then  2  x  =  the  larger  number. 

And  their  sura  is  =3  x  (or  x-\-2  x). 

But  we  know  that  their  sum        =45  (the  given  sum). 

Therefore,  3  x  =45. 

And  X  =  15,  the  smaller  number. 

Also,  2  times  the  smaller,  or  2  x  =  30,  the  larger  number. 


Results. 


19.  The  sum  of  two  numbers  is  100,  and  one  of  them  is  three 
times  the  other  one.     What  are  the  numbers  ? 

20.  Find  two  numbers,"  one  of  which  is  five  times  the  other, 
if  the  sum  of  both  numbers  is  60. 

21.  A  boy  is  three  times  as  old  as  his  sister,  and  the  sum  of 
their  ages  is  24  years      How  old  is  each? 

22.  A  man  is  three  times  as  old  as  his  boy,  and  the  sum  of  their 
ages  is  48  years.     Find  the  age  of  each. 

23.  A  man  weighs  three  times  as  much  as  his  boy,  and  together 
they  weigh  240  pounds.     Find  the  weight  of  each. 

24.  Two  boys  solved  a  number  of  problems,  and  one  solved 
twice  as  many  as  the  other.  Together  they  solved  60.  How 
many  did  each  solve? 

25.  A  man  and  a  boy  working  together  at  a  task  earned  S15. 
If  the  man  was  paid  four  times  as  much  as  the  boy  was,  how  much 
was  paid  to  each? 

26.  A  farmer  paid  $250  for  a  horse  and  a  wagon,  and  the  cost 
of  the  horse  was  four  times  the  cost  of  the  wagon.  What  was  the 
cost  of  each? 


56  THE  EQUATION 

27.  A  young  man  saved  a  certain  sum  and  bought  a  house  lot. 
Then  he  saved  five  times  as  much  and  built  a  house.  The  house 
and  the  lot  cost  him  $3000.  How  much  did  the  lot  cost?  How 
much  did  the  house  cost  ? 

IV.  Miscellaneous  Problems  for  Analysis  and  Solution  by 
Equation. 

28.  Three  times  a  given  number,  increased  by  10,  equals  25. 
Find  the  number. 

29.  Five  times  a  given  number,  increased  by  5,  equals  80. 
Find  the  number. 

30.  Four  times  a  certain  number,  decreased  by  10,  equals  50. 
Find  the  number. 

31.  Seven  times  a  certain  number,  decreased  by  11,  equals  59. 
Find  the  number. 

32.  Three  times  a  number  increased  by  5  times  the  same  num- 
ber equals  56.     Find  the  number. 

33.  Seven  times  a  number  decreased  by  four  times  the  same 
number  equals  36.     Find  the  number. 

34.  Separate  50  into  two  such  parts  that  the  larger  part  shall 
be  equal  to  four  times  the  smaller  part. 

35.  A  boy  saved  $7,  which  was  $1  more  than  twice  the  cost  of 
a  sled  he  purchased.     What  did  the  sled  cost? 

36.  A  man  gave  10  cents  to  each  of  a  number  of  boys  and  had 
30  cents  left.  If  he  had  80  cents  at  first,  how  many  boys  re- 
ceived 10  cents  each? 

37.  A  man's  salary  is  $100  and  after  paying  a  debt  of  $10  he 
deposited  five  times  the  amount  of  the  debt  in  the  bank  and  kept 
the  rest  of  his  salary  for  expenses.  How  much  did  he  keep  for 
his  expenses? 

38.  A  housekeeper  purchased  seven  dining  room  chairs  and 
gave  a  50-dollar  bill  in  payment.  She  received  in  change  thi'ee 
5-dollar  bills.     What  was  the  price  of  each  chair? 


SOLVING  PROBLEMS  BY  EQUATIONS  57 

39.  A  house  and  lot  together  cost  $4800,  and  the  house  cost 
3  times  as  much  as  the  lot.     How  much  did  the  lot  cost? 

40.  Jack  has  10  cents  more  than  Tom,  and  Tom  has  15  cents 
more  than  Harry.  If  all  three  have  $1.00,  how  many  cents  has 
each  boy? 

41.  Jerry's  father  weighs  20  pounds  more  than  3  times  as  much 
as  Jerry  weighs.  If  both  weigh  250  pounds,  how  much  does  each 
of  them  weigh  ? 

42.  Mary  made  3  times  as  many  buttonholes  as  Emily,  and 
Emily  made  3  times  as  many  as  Kate.  If  all  three  made  52 
buttonholes,  how  many  did  each  of  them  make  ? 

43.  Earl  and  Dick  had  war  gardens,  and  Earl  earned  from  his 
garden  $8  more  than  Dick  earned  from  his.  How  much  did  each 
earn,  if  both  earned  $28? 

44.  A  truck  and  its  load  of  coal  weigh  7350  pounds,  and  it  was 
found  that  the  coal  weighed  just  twice  as  much  as  the  truck. 
Find  the  weight  of  each,  and  the  number  of  tons  of  coal  in  the 
load. 

45.  On  a  pleasure  trip  a  man  travels  three  times  as  far  by  rail 
as  he  travels  by  boat,  and  the  entire  trip  is  160  miles.  What  is 
the  number  of  miles  traveled  by  rail  and  the  number  by  boat  ? 

46.  An  automobihst  finds  at  the  end  of  the  season  that  his 
expenses  for  gasoline  were  six  times  the  amount  paid  for  repairs. 
If  the  amount  paid  for  both  gasoline  and  repairs  was  $175,  how 
much  was  paid  for  each  item? 

47.  A  housekeeper  finds  that  her  annual  expenses  for  food  are 
twice  as  much  as  her  expense  for  rent,  and  that  her  expense  for 
clothing  and  for  her  maid  equals  that  paid  for  rent.  If  she  spends 
$2000  annually,  how  much  does  she  spend  for  rent,  and  for  food? 

48.  A  man  said  to  his  boy,  "  Your  age  is  twice  that  of  your 
sister *s,  and  my  age  is  equal  to  twice  the  sum  of  your  age  and 
your  sister's  age.  Also,  the  sum  of  the  ages  of  all  three  of  us  is 
54  years."  What  is  the  age  of  the  sister,  the  age  of  the  boy,  and 
the  age  of  the  man? 


PERCENTAGE 

Per  Cent  means  hundredths  or  "by  the  hundred ^ 

If  a  merchant  made  a  profit  of  $10  on  every  sale  of  $100  worth 
of  goods,  he  made  "  10  on  the  hundred,"  or  '*  10  per  cent." 

If  you  paid  $6  for  the  use  of  $100  for  a  given  length  of  time,  you 
paid  *'  6  on  the  hundred,"  or  "  6  per  cent." 

The  expression  "  per  cent  "  comes  from  the  Latin  "  per  centum," 
meaning  "  by  the  hundred." 

The  symbol  "  %  "  is  used  instead  of  the  words  "  per  cent." 

Thus  :  10  per  cent  is  written  10%. 

6  per  cent  is  written  6%. 

A  per  cent  may  be  written  in  the  form  of  a  common  fraction. 
Thus:  10%=-jU)_.=_i_ 

20%=Yoo  =  5^- 

33-  ' 

333^%  =Yqq  =  3^>  etc. 

For  the  numerator  of  the  fraction  write  the  given  number  of  hun- 
dredths.    For  the  denominator  of  the  fraction  write  100. 
Reduce  the  fraction  to  lowest  terms. 

Per  cents  may  be  written  in  the  form  of  decimals. 

Thus:       5%  =  .05,  since  "per  cent"  means  "hundredths." 
12%  =.12. 
37.5%  =  .375,  etc. 

Move  the  decimal  point  in  the  given  "per  cent  two  places  to  the  left. 
Omit  the  symbol  %. 


Read : 

1.  12%. 

2.  15%. 

3.  18%. 

4.  25%o. 


ORAL 

PRACTICE 

5. 

12i%. 

9.  62i%. 

13. 

99%. 

6. 

33x%. 

10.  75%. 

14. 

120%. 

7. 

37i%. 

11.  83i%. 

15. 

1331% 

8. 

50%. 

12.  871%. 

16. 

200%. 

58 


PER  CENTS 


55 


Give,  in  the  lowest  terms,  the  equivalent  fractions  for 


17. 
18. 
19. 
20. 


20%. 

25%. 
30%. 
35%. 


21. 
22. 
23. 
24. 


50%. 

60%. 

75%. 
80%. 


25. 
26. 
27. 

28. 


Give  the  equivalent  decimals  for : 

33.  10%o.  36.    55%.  39. 

34.  15%o.  37.    75%.  40. 

35.  20%.  38.    85%.  41. 


15%. 

24%. 
32%. 
48%. 

37i%. 
62i%. 
87i%. 


29. 
30. 
31. 
32. 

42. 
43. 
44. 


0- 


72%. 
84%. 


%. 
%. 

To  /O- 


1% 


Common  fractions  may  be  expressed  as  per  cents. 
Thus  :  -^^  may  be  written  .07  =7%. 


100 


Y^Q  may  be  ^\Titten  .19  =  19%. 
I  may  be  -WTitten  .625  =62|-%. 

Change  the  given  fractioti  to  a  decimal. 

Move  the  decimal  point  two  places  to  the  right. 

Annex  the  symbol  %. 

Decimal  fractions  may  be  expressed  in  the  form  of  per  cents. 

Thus :  .12  may  be  A\Titten  12%. 

.625  may  be  ^\Titten  62.5%,  etc. 

Move  the  decimal  point  two  places  to  the  right. 
Annex  the  symbol  %. 


Express  as  per 

cent 

ORAL 

• 
• 

PRACTICE 

1.    .10. 

9. 

.031. 

17.    i. 

25. 

H. 

2.    .25. 

10. 

.66f. 

18.    |. 

26. 

If. 

3.    .35. 

11. 

1.25. 

19.    f. 

27. 

21 

^4- 

4.    .375. 

12. 

2.75. 

20.    f. 

28. 

3f. 

5.    .875. 

13. 

3.00. 

21.    i. 

29. 

4^ 

6.    .625. 

14. 

3.25. 

22.    3. 

30. 

42 

7.    .725. 

15. 

3.125. 

23     -^- 

*^-      10- 

31. 

^ 
04. 

8.    .935. 

16. 

4.375. 

24       5 

32. 

^5 
0^. 

60 


PERCENTAGE 


Much  labor  is  saved  by  using  fractional  forms  for  the  more  com- 
mon per  cents.     The  following  equivalents  should  be  memorized  : 


TABLE   OF    EQUIVALENTS 

5%  =  4 

16|%=1 

50%    =i 

6i%=n 

20%    =\ 

62^%  =1 

8|%=  ^ 

25%    =-J 

75%    =\ 

10%  =  i 

33i%  =5 

83|%  =  I 

12^%=   8 

37i%  =1 

87^%  =1 

1. 

2. 
3. 

4. 
5. 


ORAL  PRACTICE 

What  is  ^  of  100?     .1  of  100?     10%  of  100? 
What  is  i  of  60?     .25  of  60?     25%  of  60? 
What  is  f  of  80?     .375  of  80?     37^%  of  80? 
What  is  f  of  200?     .625  of  200?     62i%o  of  200? 
What  fractional  part  of  a  yard  is  1  foot?     What  per  cent 
of  a  yard  is  1  foot? 

6.  What  fractional  part  of  a  gallon  is  1  quart?     What  per 
cent  of  a  gallon  is  1  quart  ? 

7.  What  fractional  part  of  a  foot  is  1  inch?     What  per  cent 
of  a  foot  is  1  inch? 

8.  A  man  spends  one  fifth  of  his  salary  for  rent,  and  one 
fourth  of  it  for  food.     Express  each  item  as  a  per  cent  of  his  salary. 

9.  From  12  bushels  of  seed  potatoes  a  field  produced  180  bushels 
of  potatoes.     What  per  cent  of  the  crop  was  the  seed? 

10.  A  profit  of  $300  was  made  on  a  sale  amounting  to  $1500. 
What  was  the  per  cent  of  profit  ? 

11.  Of  th^  120  spectators  at  a  ball  game,  24  were  boys.     What 
per  cent  of  the  whole  number  of  spectators  is  the  number  of  boys  *? 

12.  A  triangle  has  three  equal  sides.     What  per  cent  of  the 
perimeter  of  the  triangle  is  in  the  length  of  any  one  side  ? 


THE  FIRST  PROBLEM  IN  PERCENTAGE 


61 


THE   THREE   CASES   OF   PERCENTAGE 
I.   To  Find  a  Per  Cent  of  a  Number. 

Illustrations : 

Find  12%  of  750. 

12%  =.12. 


1.    Find  5%  of  240.     2. 


5%  =  .05. 


3.  Find  8f  %o  of  96. 
8f%=.0875. 


240 

750 

.05 

.12 

12.00 

1500 

750 

90.00 

Hence, 

Hence, 

5%  of  240  =  12. 

12% 

96 
.0875 
480 
672 

768 
8.4000 
Hence, 
750=90.  8f%  of  96=8.4. 

Express  the  given  per  cent  as  a  decimal. 
Multiply  the  given  number  by  this  decimal. 

The  number  of  which  a  per  cent  is  required        405     Base. 

is  called  the  Base.  .09     Rate. 

In  the  example  at  the  right  405  is  the  base.  36.45     Percentage, 

The  number  of  hundredths  in  the  required  per  cent  is  called  the 

Rate. 

In  the  example  9  hundredths,  or  .09,  is  the  rate. 

The  product  of  the  base  by  the  rate  is  called  the  Percentage. 

In  the  example  36.45  is  the  percentage. 


d: 

5%  of  100. 
5%  of  80. 
5%  of  90. 
5%)  of  95. 
10%  of  20( 

Rate  xBase  =  Percentage 

^in 

1. 
2. 
3. 
4. 
5. 

ORAL  PRACTICE 

2%  of  500.         8%  of  40 
2%  of  800.         8%)  of  80 
2%  of  20.           8%o  of  90 
4%  of  80.           9%o  of  60 
).         4%  of  120.         9%  of  90 

20%  of  500 
20%  of  800 
30%  of  ir 
30%of^  /O 
30%  of  400 

62 


PERCENTAGE 


Find : 

1.  5%  of  80. 

2.  6%  of  80. 

3.  6%  of  90. 

4.  7%  of  90. 

5.  15%  of  $275. 

6.  15%  of  $300. 

7.  18%  of  $320. 

8.  20%  of  $340. 


BLACKBOARD    PRACTICE 


8%  of  70. 
8%  of  95. 
9%  of  109. 
10%  of  130. 


10%  of  45. 
10%  of  110. 
12%  of  125. 
14%  of  150. 


15%  of  75. 
16%  of  120. 
20%  of  135. 
25%  of  165. 


9.  25%  of  $125.50. 

10.  28%  of  $325.75. 

11.  30%  of  $610.50. 

12.  35%  of  $670.75. 


13.  40%  of  $1250. 

14.  60%  of  $1500. 

15.  75%  of  $2150. 

16.  80%  of  $3750. 


17.  Find  10%,  20%,  40%,  and  80%  of  $1000. 

18.  Find  12i%,  25%,  37^^%,  and  50%  of  $1500. 

19.  Find  33i%,  66|%,  and  87i%  of  $2400. 

20.  Find  6i%,  8^%,  16f  %,  and  83^%  of  $2400. 

21.  Find  110%  of  $500;  125%  of  $500;  150%  of  $600. 

22.  Find  10%  of  25%  of  $200 ;  25%  of  40%  of  $2500. 


Find : 

23.   1%  of  20. 

27. 

,\%  of  100. 

31. 

f  %  of  200. 

24.   i%of30. 

28. 

,^0%  of  300. 

32. 

1%  of  200. 

25.   i%of20. 

29. 

1%  of  1200. 

33. 

1%)  of  600. 

26.   i%  of  30. 

30. 

1%  of  400. 

34. 

1%  of  900. 

WRITTEN    APPLICATIONS 

1.  Of  a  class  numbering  120  boys,  5%  failed  to  graduate. 
How  many  boys  failed  to  graduate  ? 

2.  A  house  is  valued  at  $5000  and  the  annual  rent  of  this 
house  is  8%  of  its  value.  How  much  is  the  rent  of  this  house  for 
one  year? 

3.  A  carload  of  grain  costing  $500  is  damaged  and  is  sold  at  a 
reduction  of  12^  per  cent.     How  much  is  received  for  the  grain? 

4.  A  grocer  makes  a  profit  of  8  per  cent  on  a  stock  of  goods 
that  cost  him  $9500.     What  is  the  amount  of  his  profit? 


THE  FIRST  PROBLEM  IN  PERCENTAGE  63 

5.  A  boy  bou-ght  candy  for  $9.00  and  sold  it  at  a  profit  of  12|^ 
per  cent.     Find  the  amount  of  his  profit. 

6.  An  estate  amounted  to  $24,000.  One  of  the  heirs  received 
15  per  cent  of  this  estate.     What  amount  did  he  receive? 

7.  A  house  rented  for  $20  per  month,  but  the  owner  increased 
the  rent  20  per  cent.  How  much  did  the  house  then  rent  for  per 
month  ? 

8.  A  tank  that  holds  1200  gallons  is  85  per  cent  full.  How 
many  gallons  are  in  the  tank? 

9.  540  persons  attended  a  lecture,  33|^%  of  the  number  being 
men,  50  per  cent  women,  and  the  rest  children.  Find  the  number 
of  men,  the  number  of  women,  and  the  number  of  children  that 
attended  the  lecture. 

10.  A  grocer  had  $7000  invested  in  his  business.  In  each  of 
two  successive  years  he  cleared  12^  per  cent,  and  in  the  third  year 
he  cleared  15  per  cent.     Find  the  total  profit  for  the  three  years. 

11.  A  clerk  receives  $800  for  his  first  year's  work,  but  in  each 
of  the  four  years  following  he  was  given  an  increase  of  10  per  cent 
over  the  preceding  year  Find  the  total  amount  he  earned  in 
these  five  years. 

12.  15  per  cent  of  a  man's  property  is  invested  in  real  estate, 
33^  per  cent  in  bonds,  40  per  cent  in  his  business,  and  the  rest  is 
in  the  savings  bank  The  total  value  of  his  property  is  $54,000. 
Find  the  amounts  in  each  of  his  different  mvestments,  and  also 
the  amount  he  has  in  the  savings  bank. 

13.  A  man  bought  an  automobile  for  $3000.  In  the  first  year 
that  he  ran  it  he  paid  4%  of  the  purchase  price  of  the  car  for 
gasoline  and  oil,  5%  of  the  price  for  insurance,  1%  of  it  for  a 
hcense,  and  6%  of  it  for  garage  charges.  Find  the  total  expense 
of  keeping  and  running  the  car  for  that  year. 

14.  A  family  saved  $450  in  a  year,  but  spent  the  balance  of 
their  income  as  follows:  for  rent,  25%;  for  food,  35%;  for 
clothing,  18%  ;  for  reading  and  amusements,  7%  ;  and  for  miscel- 
laneous expenses,  5%.     Find  the  amount  of  their  income. 


64 


PERCENTAGE 


II.   To  Find  the  Per  Cent  One  Number  Is  of  Another  Number. 

From  the  first  case  : 


Rate  X  Base  =  Percentage 


From  which,  by  division : 


Rate  =  Percentage  -v-  Base 


To  Find  the  Rate  Divide  the  Percentage  hy  the  Base. 

Illustration : 

1.   What  per  cent  of  60  is  15? 

The  base  is  known  to  be  60.      The  percentage  is  known  to  be  15. 

Applying  the  rule :     Percentage  =1^  =  1      25  or  25%.     The  Rate. 

Base  60      4 

You  should  note  that  the  process  gives  the  decimal  expression 
of  the  fractional  relation  of  the  two  given  numbers. 

ORAL  PRACTICE 

1.  What  part  of  20  is  2?     How  many  hundredths  of  20  is  2? 
What  per  cent  of  20  is  2  ? 

2.  What  part  of  100  is  25  ?     How  many  hundredths  of  100  is  25  ? 
What  per  cent  of  100  is  25  ? 

3.  What  part  of  150  is  30?     How  many  hundredths  of  150  is 
30?     What  per  cent  of  150  is  30? 

What  per  cent  of 


4. 

5  is  4? 

9. 

12  is  4? 

14. 

120  is  40? 

19. 

$9  is  $3  ? 

5. 

6  is  3? 

10. 

36  is  6? 

15. 

144  is  18? 

20. 

$18  is  $9? 

6. 

8  is  6? 

11. 

45  is  9? 

16. 

160  is  10? 

21. 

$54  is  $9? 

7. 

9  is  3? 

12. 

54  is  18? 

17. 

210  is  70? 

22. 

$72  is  $27? 

8. 

15  is  3? 

13. 

63  is  21? 

18. 

300  is  100? 

23. 

$85  is  $17? 

THE  SECOND  PROBLEM  IN  PERCENTAGE  65 

BLACKBOARD   PRACTICE 

What  per  cent  of 

1.  30  is  6?  30  is  10?  40  is  10?  60  is  12? 

2.  40  is  5?  40  is  8?  40  is  20?  75  is  15? 

3.  50  is  10?  75  is  20?  80  is  32?  90  is  50? 

4.  125  is  50?  125  is  75?  125  is  100?  125  is  125? 

5.  128  is  8?  156  is  13?  250  is  12i?  350  is  175? 

6.  150  is  30?  180  is  36?  200  is  40?  240  is  48? 

7.  225  is  75?  256  is  16?  324  is  81?  520  is  5.2? 

8.  250  is  12.5?  375  is  7.5?  4200  is  84?  4200  is  8.4? 

9.  300  is  120?  300  is  180?  300  is  225?  4500  is  1350? 

To  the  nearest  tenth,  what  per  cent  of 

10.  27  is  13?  35  is  14?  42  is  12?  54  is  16? 

11.  35  is  15?  46  is  19?  54  is  19?  54  is  25? 

12.  64  is  18  ?  69  is  24  ?  74  is  19  ?  82  is  40  ? 

13.  92  is  21?  95  is  29?  110  is  37?  120  is  44? 

14.  110  is  31?  120  is  35?  145  is  53?  160  is  56? 

15.  $25  is  $11?         $75  is  $32?        $90  is  $17?      $100  is  $19? 

16.  $35.50  is  $11.35?     $47.10  is  $13.25?       $54.65  is  $11.75? 

17.  $125.50  is  $8.19?     $256.75  is  $111.25?  $1565.50  is  $125.00? 

WRITTEN   APPLICATIONS 

1.  A  baseball  team  won  75  games  of  the  125  games  played. 
What  per  cent  of  the  total  number  of  games  played  was  the  num- 
ber won? 

2.  A  boy  weighed  100  pounds  last  year,  but  at  the  present 
time  his  weight  is  120  pounds.  What  per  cent  of  his  present 
weight  is  his  former  weight? 

3.  From  a  salary  of  $1500  a  clerk  saved  in  one  year  $300. 
What  per  cent  of  his  salary  did  he  save? 

4.  A  dairyman  kept  80  cows  last  year  but  has  100  at  the 
present  time.  By  what  per  cent  did  he  increase  the  number  kept 
last  year  to  give  the  number  he  has  now  ? 


66  PERCENTAGE 

5.  A  horse  that  cost  a  dealer  $160  was  sold  for  $200.  What 
was  the  gain  m  dollars?     What  was  the  per  cent  of  gain? 

6.  A  farm  of  200  acres  is  so  divided  that  40  acres  are  in  pasture. 
What  per  cent  of  the  whole  farm  is  the  pasture  ? 

7.  A  baseball  team  won  42  games  and  lost  14.  What  per 
cent  of  the  total  number  of  games  played  is  the  number  of  games 
won? 

8.  A  club  with  a  membership  of  30  admits  5  new  members. 
What  per  cent  of  the  new  membership  is  the  former  membership  ? 

9.  A  contractor  is  paid  $600  when  he  begins  the  construction 
of  a  dwelling  that  is  to  cost  $3600.  What  per  cent  of  the  total 
cost  is  this  payment? 

10.  A  mixture  of  1400  cubic  feet  of  concrete  contains  200 
pounds  of  cement.     AYliat  per  cent  of  the  mixture  is  the  cement? 

11.  65%  of  the  cost  of  a  house  and  lot  was  spent  on  the  house. 
If  the  house  and  lot  cost  $8000,  find  the  cost  of  the  lot  and  the 
cost  of  the  house. 

12.  A  cow  gave  16,257  pounds  of  milk  in  one  year,  and  her  milk 
was  found  to  contain  642  pounds  of  butter  fat.  What  was  the  per 
cent  of  butter  fat  in  her  milk  ? 

13.  A  corporation  had  $150,000  invested  in  their  plant  and  in 
one  year  they  sold  $250,000  worth  of  their  product.  What  per 
cent  of  their  investment  was  their  sales  ? 

14.  A  real  estate  broker  received  $1750  as  his  commission  for 
selhng  a  business  block.  If  the  block  sold  for  $35,000,  what  was 
the  rate  per  cent  of  his  commission? 

15.  A  man  who  failed  in  business  paid  $2437.50  on  a  debt 
amounting  to  $3750.  What  per  cent  of  the  whole  amount  did  he 
pay?     How  many  ''  cents  on  the  dollar  J'  did  he  pay? 

16.  A  business  man  made  a  total  profit  of  $15,000  in  one  year, 
but  his  expenses  were  $7500  for  help,  $1800  for  rent,  and  $1200 
for  miscellaneous  items.  Find  the  per  cent  of  his  total  profits 
that  was  left  after  paying  his  expenses. 


THE  SECOND  PROBLEM  IN  PERCENTAGE  67 

• 

17.  70%  of  a  journey  of  1200  miles  was  made  by  water,  and 
the  rest  of  it  was  made  by  rail.  How  many  miles  were  traveled 
by  rail? 

18.  A  painter  can  paint  a  barn  in  12  days.  What  per  cent  of 
it  can  he  paint  in  5  days?  What  per  cent  in  3  days?  What  per 
cent  in  7  days  ?     What  per  cent  in  1 1  days  ? 

19.  A  broker  failed  and  the  total  amount  of  his  debts  was 
$120,000.  If  the  total  value  of  his  property  is  $80,000,  what  per 
cent  of  his  debts  can  be  paid  with  his  property  ? 

20.  From  a  crop  of  1200  bushels  of  potatoes  a  farmer  sold  400 
bushels  to  hotels,  600  bushels  to  grocers,  and  the  rest  to  individuals. 
What  per  cent  of  the  whole  crop  did  he  sell  individually?  To 
grocers?     To  hotels? 

21.  A  man  bought  a  lot  for  $1500  and  built  a  house  on  it  cost- 
ing $6000.  What  per  cent  of  the  cost  of  the  house  is  the  cost  of 
the  lot?  What  per  cent  of  the  total  cost  of  the  house  and  lot  is 
the  cost  of  the  house  ? 

22.  A  salesman  is  offered  a  salary  of  $2000,  and  in  addition 
he  is  promised  $100  commission  for  every  $10,000  worth  of 
goods  he  sells  during  the  year.  He  sells  goods  worth  $120,000. 
What  per  cent  of  his  salary  is  the  amount  he  receives  in  com- 
missions ? 

23.  A  man  paid  $6000  for  a  house.  His  annual  expenses  for 
maintaining  and  owning  it  included  $180  for  interest,  $75  for 
taxes,  and  $20  for  water.  What  per  cent  of  the  cost  of  the  house 
is  the  amount  of  these  three  items? 

24.  In  a  league  of  four  baseball  teams  the  standing  on  a  certain 
day  was  obtained  from  the  following :  The  Crescents  had  won 
24  games  and  had  lost  10 ;  the  Stars  had  won  25  and  had  lost  11 ; 
the  Imperials  had  won  20  and  had  lost  13 ;  and  the  Orioles  had 
won  26  and  lost  8.  Find  the  total  number  of  games  each  team 
played  and  the  per  cent  of  games  won  by  each  team. 


68 


PERCENTAGE 


in.   To  Find  the  Number,  of  which  a  Given  Niunber  is  a  Given 
Per  Cent. 

From  the  first  case  : 


Rate  X  Base  =  Percentage 


By  Division 


Base  =  Percentage  -r-  Rate 


To  Find  the  Base,  Divide  the  Percentage  hy  the  Rate. 

Illustrations : 

1.  8%  of  a  number  is  60.     What  is  the  number? 

Since  8%  of  the  number  is  60, 

1  %  of  the  number  is  60-^8  =7.5. 
Hence,  100%,  or  the  required  number,     100x7.5=750.     Result. 

2.  Find  the  number  of  which  540  is  12i%. 

Since  12^%  of  the  number  is  540, 

1%  of  the  number  is  540-^12^=43.2. 
Hence,  100%,  or  the  required  number,  100X43.2  =4320.     Result. 


ORAL  PRACTICE 

Find  the  number  of  which 

1. 

10  is  10%. 

11. 

25  is  121%. 

21. 

60  is  331%. 

2. 

15  is  10%. 

12. 

30  is  12i%. 

22. 

66  is  371%. 

3. 

20  is  10%. 

13. 

35  is  20%. 

23. 

70  is  70%. 

4. 

10  is  20%. 

14. 

40  is  25%. 

24. 

80  is  80%. 

5. 

15  is  20%. 

15. 

40  is  20%. 

25. 

100  is  16f% 

6. 

20  is  20%. 

16. 

40  is  40%. 

26. 

120  is  331% 

7. 

10  is  25%. 

17. 

50  is  33i%. 

27. 

150  is  50%. 

8. 

15  is  25%. 

18. 

60  is  621%. 

28. 

160  is  80%. 

9. 

20  is  25%. 

19. 

60  is  16f  %. 

29. 

270  is  90%. 

10. 

25  is  25%. 

20. 

75  is  371%. 

30. 

240  is  120% 

THE  THIRD  PROBLEM  IN  PERCENTAGE 


69 


BLACKBOARD    PRACTICE 

FiiK 

i  the  number  of  which 

1. 

50  is  25%. 

75  is  50%. 

125  is  50%. 

150 

is  60%. 

2. 

60  is  20%. 

80  is  40%. 

100  is  60%. 

180 

is  90%. 

3. 

60  is  30%. 

80  is  50%. 

140  is- 50%. 

210 

is  60%. 

4. 

75  is  50%. 

100  is  33i%. 

180  is  60%. 

240 

is  62i% 

5. 

75  is  60%. 

90  is  75%. 

144  is  80%. 

180 

is  62^% 

6. 

50  is  12i%. 

75  is  33i%. 

125  is  62i%. 

200 

is  125% 

7. 

75  is  S7i%. 

100  is  67i%. 

180  is  90%. 

210 

is  105% 

8. 

90  is  40%. 

120  is  60%. 

240  is  80%. 

250 

is  120% 

9. 

120  is  100%. 

125  is  60%. 

190  is  95%. 

250 

is  200% 

10. 

120  is  150%. 

135  is  67^%. 

175  is  100%. 

275 

is  200% 

11. 

200  is  100%. 

225  is  112i%. 

250  is  125%. 

350 

is  200% 

WRITTEN   APPLICATIONS 

1.  If  12  boys  join  a  class,  and  this  number  is  20%  of  the 
original  class,  how  many  were  in  the  original  class? 

2.  A  man  gains  15  pounds,  which  is  12%  of  his  former  weight. 
How  much  was  his  former  weight  ? 

3.  A  house  is  sold  at  a  loss  of  $500,  which  is  12j-%  of  the  cost 
of  it.     How  much  did  the  house  cost? 

4.  After  forty-five  miles  of  a  telephone  Hne  is  completed  the 
builder  reports  that  85%  still  remains  to  be  built.  How  long 
will  the  line  be  when  it  is  completed  ? 

5.  After  twelve  tenants  had  moved  into  a  new  apartment 
house,  33^%  of  the  entire  capacity  of  the  house  was  still  vacant. 
How  many  more  tenants  can  the  house  accommodate? 

6.  420  bushels  of  corn  are  sold  by  a  dealer,  which  was  30% 
of  the  entire  stock  he  had  on  hand.  How  many  bushels  of  corn 
did  he  have  at  first  ?     How  many  bushels  has  he  left  ? 

7.  A  horse  was  sold  for  $200,  which  was  120%  of  the  amount 
paid  for  him.  How  much  was  paid  for  him  ?  How  much  was  the 
profit  on  the  sale  ?     What  was  the  per  cent  of  profit  on  the  sale  ? 


70  PERCENTAGE 

8.  A  merchant  paid  bills  amounting  to  $960,  and  this  sum 
was  only  62^%  of  the  total  amount  he  owed.  What  was  the 
total  amount  of  his  indebtedness?  What  per  cent  of  it  remains 
unpaid  ? 

9.  A  baseball  team  lost  48  games  in  an  entire  season,  and  this 
number  was  37^%  of  the  total  number  of  games  played.  Find 
the  total  number  of  games  played,  and  the  total  number  won. 

10.  A  man  bought  a  lot  and  built  a  house  on  it  that  cost  him 
$7500.  The  cost  of  the  house  was  83J%  of  the  total  cost  of  both 
the  house  and  the  lot.     How  much  was  the  cost  of  the  lot? 

11.  A  merchant's  total  sales  for  a  year  amounted  to  $49,650, 
and  his  expenses  for  running  the  business  were  $5650.  His  sales, 
less  his  expenses,  were  110%  of  the  amount  paid  for  his  goods. 
How  much  was  his  profit  for  the  year? 

GENERAL  REVIEW  OF  PERCENTAGE 


ORAL  PRACTICE 

Find : 

1. 

10%  of  20. 

7. 

25%  of  36. 

13. 

16|%  of  60. 

2. 

20%  of  10. 

8. 

40%  of  70. 

14. 

33i%  of  75. 

3. 

10%  of  50. 

9. 

50%  of  80. 

15. 

37i%  of  80. 

4. 

50%  of  10. 

10. 

60%  of  70, 

16. 

621%  of  80. 

5. 

10%  of  90. 

11. 

70%  of  90. 

17. 

831%  of  96. 

6. 

Wh 

90%  of  10. 
at  per  cent  of 

12. 

80%  of  100. 

18. 

971%  of  140. 

i 

19. 

10  is  5? 

25. 

50  is  30? 

31. 

90  is  60? 

20. 

10  is  8? 

26. 

54  is  36? 

32. 

100  is  80? 

21. 

15  is  10? 

27. 

60  is  40? 

33. 

100  is  61? 

22. 

20  is  10? 

28. 

70  is  35? 

34. 

100  is  121? 

23. 

30  is  10? 

29. 

75  is  15? 

35. 

100  is  16|? 

24. 

30  is  15? 

30. 

75  is  25? 

36. 

100  is  331? 

GENERAL  REVIEW  OF  PERCENTAGE 


71 


Find  the  number  of  which 


37.  20  is  10%". 

38.  30  is  10%. 

39.  40  is  10%. 

40.  40  is  20%. 

41.  50  is  20%. 

42.  60  is  25%. 


43.  10  is  12^%. 

44.  15  is  121%. 

45.  20  is  16|%. 

46.  30  is  16|%. 

47.  48  is  12^%. 

48.  48  is  16|%. 


49.  60is37i%,. 

50.  70  is  33^%. 

51.  75  is  62^%. 

52.  80  is  62^%. 

53.  100  is  66|%. 

54.  125is83i%j. 


BLACKBOARD   PRACTICE 


Find,  to  the  nearest  .01 


1. 

6i%  of  25. 

7. 

81%  of  50. 

13. 

121-%  of 

75. 

2. 

6i%  of  35. 

8. 

81%)  of  75. 

14. 

12i%  of 

90. 

3. 

01%  of  45. 

9. 

S0C  of  90. 

15. 

12i%  of 

105 

4. 

6^%  of  55. 

10. 

&i%  of  105. 

16. 

12^%  of 

115 

5. 

6i%  of  G5. 

11. 

81%  of  115. 

17. 

121%  of 

130 

6. 

61%o  of  75. 

12. 

81%  of  125. 

18. 

m%  of 

145 

19. 

161%)  of  50. 

25. 

331%  of  50. 

31. 

621%  of 

75. 

20. 

16|%  of  75. 

26. 

331%  of  70. 

32. 

62i%  of 

90. 

21. 

16§-%  of  85. 

27. 

331%  of  80. 

33. 

62i%  of 

105 

22. 

16|%o  of  90. 

28. 

331  %  of  95. 

34. 

62i%  of 

115 

23. 

16J%  of  95. 

29. 

331%  of  110. 

35. 

621-%  of 

130 

24. 

16|%o  of  105. 

30. 

33i%  of  115. 

36. 

62i%  of 

145 

37. 

83^%  of  60. 

42. 

83i%o  of  90. 

47. 

87^%  of 

120 

38. 

831-%  of  65. 

43. 

831%  of  95. 

48. 

m%  of 

125 

39. 

83i%o  of  70. 

44. 

83i%o  of  105. 

49. 

871%  of 

130 

40. 

83^%o  of  75. 

45. 

871-%  of  105. 

50. 

87i%  of 

135 

41. 

83i%o  of  80. 

46. 

871-%  of  110. 

51. 

871-%  of 

140 

52.  105%o  of  $50. 

53.  110%)  of  $75. 

54.  115%  of  $90. 

55.  120%  of  $100. 


56.  120%  of  $40.50. 

57.  125%  of  $56.15. 

58.  125%  of  $62.50. 

59.  106^%)  of  $25.00. 


72 


PERCENTAGE 


60.  125%  of  $110. 

61.  125%  of  $125. 

62.  105%  of  $15.50. 

63.  110%  of  $20.25. 

64.  115%  of  $35.10. 

70.  5%  of  10%  of  $50. 

71.  5%  of  10%  of  $75. 

72.  5%  of  10%  of  $100. 

73.  10%  of  20%  of  $100 

74.  10%  of  25%  of  $120 

What  per  cent  of 

80.  250  is  25?        90. 

81.  450  is  50?        91. 

82.  550  is  110?      92. 

83.  625  is  125?      93. 

84.  750  is  150?      94. 

85.  800  is  160?      95. 

86.  990  is  200?      96. 

87.  1200  is  240?    97. 

88.  1350  is  270?    98. 

89.  1500  is  450?    99. 


65.  112i%  of  $35.50. 

66.  112|%  of  $50.75. 

67.  137i%  of  $125.50. 

68.  137i%  of  $162.50. 

69.  162i%  of  $162.*50. 

75.  10%  of  30%  of  $125.50. 

76.  15%  of  30%  of  $250.00. 

77.  20%  of  30%  of  $375.00. 

78.  30%  of  50%  .of  $500.00. 

79.  40%  of  50%  of  $1000.00. 


$50  is  $12.50?  100.  $12.40  is  $3.10? 

$90  is  $12.50?  101.  $18.75  is  $3.75? 

$100  is  $12.50?  102.  $22.50  is  $4.50? 

$125  is  $12.50?  103.  $37.50  is  $6.7^5? 

$150  is  $16.25?  104.  $50.00  is  $6.25? 


$175  is  $18.75?  105. 

$225  is  $27.50?  106. 

$250  is  $32.50?  107. 

$300  is  $37.50?  108. 

$400  is  $62.50?  109. 


$62.50  is  $6.25? 
$75.00  is  $12.50? 
$87.50  is  $37.50? 
$112.50  is  $37.50? 
$137.50  is  $62.50? 


Find  the  number  of  which 


110.  42  is  15%.  114. 

111.  65  is  20%.  115. 

112.  90  is  18%.  116. 

113.  120  is  25%.  117. 


12.5  is  10%. 

15.6  is  25%. 
125.7  is  30%. 
225.25  is  40%. 


118.  .15  is  25%. 

119.  .004  is  20%. 

120.  .117  is  37i%. 

121.  .0025  is  62|%. 


Find  the  amount  of  which 

122.  $1.25  is  8%. 

123.  $2.75  is  10%. 

124.  $3.50  is  12i%. 

125.  $4.50  is  20%. 

126.  $12.00  is  12^%. 


127.  $50.00  is  621%. 

128.  $75.00  is  80%. 

129.  $225.00  is  16|%. 

130.  $375.00  is  33i%. 

131.  $625.00  is  62i%. 


EVERYDAY  USES  FOR  PERCENTAGE        73 

WRITTEN   APPLICATIONS 

The  Use  of  Percentage  in  Everyday  Life 

I.   The  Business  Man's  Problems  in  Percentage. 

1.  A  grocer  makes  an  annual  profit  of  S3000,  which  is  15% 
of  the  total  amount  of  business  that  he  transacts.  What  amount 
of  business  does  he  transact  in  one  year? 

2.  A  merchant  does  an  annual  business  of  $27,500,  and  loses 
in  poor  accounts  $550.  What  per  cent  of  the  amount  of  business 
he  does  is  the  amount  that  he  loses? 

3.  A  real  estate  firm  sold  i  of  a  building  tract  of  120  acres  to 
one  man,  and  i  of  it  to  another  man.  What  per  cent  of  the  tract 
was  left  unsold  ? 

4.  From  a  field  containing  15  acres  and  costing  $4200  a  single 
acre  is  sold  at  a  profit  of  15%.  What  amount  is  received  for  the 
acre  sold  ? 

5.  On  a  bill  of  goods  amounting  to  $780,  a  freight  bill  of  $16, 
and  a  cartage  charge  of  $23,  were  paid.  What  per  cent  of  the  bill 
were  the  freight  and  cartage  charges  ? 

6.  A  grocer  paid  $3.84  for  a  crate  of  strawberries  containing 
32  quarts.  If  he  sold  them  for  15  cents  a  quart,  what  per  cent 
of  the  cost  price  was  his  profit  ?  What  per  cent  of  the  selling  price 
was  his  profit? 

7.  A  merchant  sold  a  piano  for  $75  less  than  the  marked  price. 
If  this  reduction  was  20%  of  the  marked  price,  what  was  the 
marked  price  ?  How  much  did  he  receive  for  the  piano  ?  If  his 
profit  was  20%  on  the  cost,  how  much  did  the  piano  cost  him? 

8.  A  clerk  received  an  increase  of  20%  in  his  salary,  and  he 
observed  that  if  the  increase  had  been  30%  instead  of  20%,  it 
would  have  given  him  $200  additional.  What  was  the  amount 
of  his  original  salary? 


74  PERCENTAGE 

9.  What  is  the  amount  saved  on  140  tons  of  coal,  when  a 
reduction  of  5%  is  made  by  the  dealer  from  the  regular  price  of 
$6.75  per  ton?     How  much  is  the  saving  per  ton? 

10.  A  speculator  in  land  increased  his  holdings  30%.  He  then 
sold  20%  of  all  his  holdings  and  had  left  1300  acres.  How  many 
acres  did  he  hold  at  first,  and  how  many  acres  did  he  sell?  \ 

11.  A  dealer  sold  a  case  of  60  bars  of  soap  for  $3.00,  and  his 
profit  on  the  sale  was  20%.  What  was  the  price  he  paid  per  bar? 
What  was  the  price  he  received  per  bar  ? 

12.  A  merchant  failed  in  business  owning  property  amounting 
to  $45,600,  and  owing  debts  amounting  to  $67,500.  The  cost  of 
settling  his  business  was  $600.  What  per  cent  did  his  creditors 
lose? 

13.  A  secretary's  salary  in  1916  was  $1800.  In  1917  his  salary 
was  increased  25%,  but  in  1918  it  was  decreased  25%  because  of 
poor  business.  What  amount  did  he  receive  in  1918?  What 
per  cent  of  his  1916  salary  was  his  1918  salary? 

14.  A  merchant's  expenses  for  the  year  were  $1875.  His  coal 
bill  was  25%  of  his  total  expense,  and  was  also  15%  of  his  total 
profits.     How  much  was  his  profit  on  the  year's  business? 

15.  During  his  second  year  in  business  a  merchant's  sales  in- 
creased 20%  over  the  first  year ;  in  his  third  year  the  increase 
was  30%  over  the  first  year's  sales,  and  in  the  fourth  year  25% 
over  the  first  year's  sales.  The  sales  in  the  first  year  amounted 
to  $12,000.  How  much  were  his  total  sales  during  the  four 
years  ? 

16.  37^%  of  2400  yards  of  cloth  were  sold  at  $1.40  per  yard; 
25%  of  it  at  $1.60  per  yard,  and  the  rest  of  it  at  $1.50  per  yard. 
How  much  was  received  for  the  entire  lot?  How  much  was  the 
profit  on  the  lot  if  the  cost  of  the  cloth  was  $1.25  per  yard? 

17.  $4.20  per  barrel  is  paid  for  flour  at  the  mill  and  the  freight 
charge  is  $.12^  per  barrel.  The  flour  is  sold  for  $5.00  per  barrel. 
What  is  the  per  cent  of  profit  made  on  the  flour?  What  per  cent 
of  the  cost  of  the  flour  is  the  freight  charge? 


EVERYDAY  USES  IN  PERCENTAGE  75 

n.   The  Farmer's  Problems  in  Percentage. 

18.  From  a  crop  of  potatoes  85%,  or  1190  bushels,  were  sold  at 
.65  per  bushel,  and  the  rest  at  S0.55  per  bushel.     How  much 

was  the  total  received  for  them? 

19.  630  bushels  of  wheat  were  sold  from  a  crop,  and  70%  of  the 
whole  crop  remained  unsold.  How  many  bushels  were  there  in 
the  whole  crop? 

20.  A  farmer  sold  a  colt  for  $240,  and  the  buyer  resold  the  colt 
at  a  profit  of  $50.  What  per  cent  of  profit  did  the  buyer  make 
on  the  purchase? 

21.  A  hog  weighed  240  pounds  live  weight,  and  dressed  80% 
of  that  amount.  At  $14.40  per  hundredweight  alive,  how  much 
is  it  worth  per  pound  dressed  ? 

22.  A  farmer  sprayed  one  half  of  a  field  of  potatoes  and  the 
yield  from  this  pai-t  was  308  bushels.  From  the  unsprayed  half 
of  the  same  field  he  obtained  140  bushels.  What  was  the  per 
cent  gained  by  spraying? 

23.  Two  steers  weighed  1100  pounds  each,  live  weight.  The 
dressed  weight  of  one  of  them  was  62%  of  the  five  weight,  and  the 
dressed  weight  of  the  other  was  51%  of  its  live  weight.  At  11^^ 
per  pound  dressed  weight,  how  much  did  both  bring? 

24.  The  lumber  and  other  materials  for  a  small  barn  cost  a 
farmer  $368.75,  and  the  labor  for  erecting  it  cost  him  $165.  What 
per  cent  of  the  total  cost  of  the  finished  barn  was  the  amount  paid 
for  the  labor? 

25.  For  a  ton  of  fertilizer  a  farmer  used  1200  pounds  of  bone, 
500  pounds  of  sulphate  of  ammonia,  and  300  pounds  of  muriate  of 
potash.     Find  the  percentage  of  each  of  the  three  ingredients. 

26.  For  one  of  his  crops  the  farmer  who  made  the  fertilizer 
in  example  25  used  200  pounds  of  this  fertilizer  to  the  acre.  What 
amount  of  each  ingredient  did  he  use  for  each  acre? 


76  PERCENTAGE 

27.  A  ton  of  a  fertilizer  is  to  contain  2%  of  r.itrogen  and  8% 
of  phosphoric  acid.  The  nitrogen  will  cost  the  farmer  16f^  per 
pound,  and  the  phosphoric  acid  6^  per  pound.  How  much 
will  the  nitrogen  and  the  acid  together  cost  for  the  ton  of 
fertilizer  ? 

28.  Potatoes  have  been  found  to  remove  from  the  soil  .2%  of 
their  weight  in  nitrogen.  How  many  pounds  of  nitrogen  at  this 
rate  will  be  removed  from  the  soil  by  a  crop  of  500  bushels  of 
potatoes?     (60  pounds  per  bushel.) 

29.  Corn  is  known  to  remove  from  the  soil  1.9%  of  its  weight 
in  nitrogen,  and  wheat  removes  2.4%  of  its  weight  in  nitrogen. 
How  many  pounds  of  nitrogen  were  removed  from  a  field  yielding 
2  tons  of  corn  and  1.5  tons  of  wheat? 

30.  A  cow  gives  7200  pounds  of  milk  in  a  year,  which  tests 
3.3%  of  butter  fat ;  another  cow  gives  5400  pounds  of  milk,  which 
tests  5.1%  of  butter  fat.  Of  these  two  cows  which  is  the  more 
profitable,  considering  only  the  butter  fat  ? 

31.  Each  of  two  cows  in  a  herd  produced  4500  pounds  of  milk 
in  one  year.  One  cow's  milk  tested  3.3%  butter  fat,  and  the 
other's  milk  tested  5.4%.  Find  the  difference  in  the  amount  of 
butter  fat  produced  by  these  two  cows. 

32.  In  a  herd  of  32  cows,  18  gave  40  pounds  of  milk  each  daily, 
9  gave  30  pounds  each  daily,  and  5  gave  22  pounds  each  daily. 
The  milk  from  the  whole  herd  averaged  3.6%  butter  fat.  Find 
the  total  quantity  of  butter  fat  produced  daily. 

33.  In  a  herd  of  20  cows,  8  gave  40  pounds  of  milk  each  daily, 
7  gave  30  pounds  each  daily,  and  5  gave  24  pounds  each  daily. 
The  first  group  '^  tested  "  5.2%,  the  second  group  4.5%,  and  the 
third  group  3.6%.  Find  the  total  number  of  pounds  of  butter 
fat  produced  daily  by  this  herd. 

34.  Because  of  the  salt,  water,  etc.,  a  pound  of  butter  fat  has 
been  found  to  make,  on  the  average,  IJ  pounds  of  butter.  At 
55  ff  per  pound  what  is  the  value  of  the  butter  produced  from  5000 
pounds  of  milk  that  tests  5.4%  butter  fat  ? 


PROFIT  AND  LOSS  77 

PROFIT   AND   LOSS 

The  Cost  of  an  article,  in  a  business  sense,  is  the  amount  paid 
for  it. 

The  Selling  Price  of  an  article  is  the  amount  received  for  it. 

A  book  is  purchased  for  $1.00,  and  is  sold  for  $1.25. 

The  cost  of  the  book  is  $1.00. 

The  selling  price  of  the  book  is  $1.25. 

The  Profit  on  a  sale  is  the  amount  by  which  the  seUing  price 
exceeds  the  cost  price. 

The  profit  in  the  illustration  is  $1.25 -$1.00  =  $.25. 

The  Loss  on  a  sale  is  the  amount  by  which  the  cost  price  ex- 
ceeds the  selling  price. 

If  the  book  in  the  illustration  had  been  sold  for  $0.80,  the  loss 
on  the  transaction  would  have  been  $1.00  — $.80  =  $.20. 

Problems  in'  Profit  and  Loss  are  merely  problems  in  percentage 
in  which 

The  Base  is  the  cost. 

The  Rate  is  the  per  cent  of  gain  or  of  loss. 

The  Percentage  is  the  profit  or  the  loss. 

Business  Practice  in  Profit  and  Loss.  In  ordinary  business 
practice  it  is  almost  a  universal  custom  to  figure  the  profits  on 
the  gross  cost  of  the  article  sold.  The  gross  cost  includes  the 
actual  cost  of  the  article  itself,  together  with  such  expense  as 
freight,  cartage,  insurance,  selling  expense,  etc. 

Illustration : 

15  rugs  at  $16  each,  cost  at  the  factory $240.00 

Freight  on  same ...  8.00 

Cartage  on  same 1.00 

Selling  expense  (estimated  from  known  experience),  4%    .     .     .  9.60 

Gross  cost $258.60 

Gross  cost  of  1  rug  =  $258.60  -4- 15  =  $17.24. 

Suppose  the  dealer  desires  a  profit  of  25%  on  this  cost. 

SeUing  Price  =$17.24 +  (25%  of  $17.24)  =$17.24+$4.31  =$21.55. 


78  PERCENTAGE 

Many  large  firms  and  department  stores  vary  the  practice  to 
avoid  complicated  bookkeeping,  as  will  be  shown  later  on. 

For  convenience  and  brevity  in  memorizing  the  principles  that 
govern  problems  in  profit  and  loss,  they  may  be  stated  as  follows . 

For  Profit : 


Rate  of  Gain  X  Cost  =  Gain.  (1) 

(100%+Rate  of  Gain)  X  Cost  =  Selling  Price.     (2) 


For  Loss 


Rate  of  Loss  X  Cost  =  Loss.  (3) 

(100%-Rate  of  Loss) X Cost  =  Selling  Price.     (4) 


Applications  of  these  principles. 
Illustration  of  (1) : 

At  a  rate  of  25  %  find  the  gain  on  a  book  costing  $2.00. 
25%  of  $2,  or  .25  X$2.00  =$0.50.     Gain. 

Illustration  of  (2) : 

Find  ths  seU'ng  price  of  a  book  that  cost  $2.00  if  th^  gain  is  25%. 
100%+25%=125%.    125%  =  1.25.    1.25  X $2.00  =$2.50.    Selling  Price. 

Illustration  of  (3)  : 

At  a  rate  of  25%  find  the  loss  on  a  book  costing  $2.00. 
25%  of  $2,  or  .25x$2.00-$0.50.     Loss. 

Illustration  of  (4)  : 

Find  the  selling  price  of  a  book  that  cost  $2.00  if  the  loss  is  25%. 
100%  -25%  =75%  =.75.     .75  X$2.00  =$1.50.     Selling  Price. 


PROFIT  AND  LOSS 


79 


1. 

2. 
3. 
4. 
5. 
6. 


$40  at  10%. 
$60  at  10%. 

$65  at  12%. 
$75  at  15%. 
$90  at  20%. 
$95  at  20%. 


13.  $125.50  at  5%^. 

14.  $240.25  at  8%. 

15.  $360.75  at  7%. 

16.  $4500.00  at  12^%. 

17.  $20,000  at  16%). 

18.  $35,000  at  25%. 


BLACKBOARD   PRACTICE 

With  the  rate  indicated,  find  the  amount  of  profit  on  goods 
costing 

7.  $100  at  12i%o. 

8.  $125  at  16|%. 

9.  $150  at  15%. 

10.  $200  at  20%. 

11.  $275  at  15%. 

12.  $350  at  25%o. 

With  the  rate  of  profit  as  indicated,,  find  the  selHng  price  of 
goods  costing 

25.  $200  at  10%o.  31. 

26.  $250  at  15%.  32. 

27.  $300  at  12^%o-  33. 

28.  $400  at  16f  %o.  34. 

29.  $450  at  20%).  35. 

30.  $750  at  25%o-  36. 

Find  the  amount  of  the  loss  when  the  selling  price  of  goods 
costing 


19. 
20. 
21. 
22. 
23. 
24. 


$100  at  15%. 
$125  at  20%. 
$130  at  16%. 
$160  at  25%. 
$190  at  20%). 
$200  at  15%o. 


$245.50  at  12%o. 
$375.20  at  15%. 
$454.95  at  15%. 
$580.61  at  20%o. 
$7500.00  at  20%o. 
$12,750  at  33^%. 


37.  $500  is  reduced  10%. 

38.  $600  is  reduced  15%. 

39.  $750  is  reduced  15%. 

40.  $900  is  reduced  20%. 

41.  $925  is  reduced  25%. 

42.  $975  is  reduced  30%. 


43.  $1275.50  is  reduced  10%). 

44.  $2450.75  is  reduced  12i%. 

45.  $3575.25  is  reduced  16f%. 

46.  $4110.75  is  reduced  16f%. 

47.  $25,750.00  is  reduced  33^%. 

48.  $27,580.00  is  reduced  37^%. 


Find  the  selling  price  when  goods  costing 


49.  $1200  are  reduced  15%c.  55. 

50.  $1500  are  reduced  12^%.  56. 

51.  $1750  are  reduced  15%.  57. 

52.  $2500  are  reduced  15%o.  58. 

63.  $3750  are  reduced  15%.  59. 

64.  $4250  are  reduced  20%.  60. 


$1250.50  are  reduced  10%. 
$1975.50  are  reduced  12^%)- 
$2150.80  are  reduced  12|-%. 
$3675.20  are  reduced  15%. 
$5490.50  are  reduced  15%. 
$6252.75  are  reduced  16f  %>. 


80 


PERCENTAGE 


APPLICATIONS   OF  PROFIT  AND  LOSS  IN  BUSINESS 

I.   To  Find  the  Cost  of  Goods  When  the  Actual  Gain  or  Loss^ 
and  the  Rate  of  Gain  or  Loss  are  Known. 

We  have  learned  that     Rate  of  Gain  X  Cost  =  Gain. 

From  which 


Gain 


Rate  of  Gain 


=  Cost. 


Application  :  ■ 

What  is  the  cost  of  goods  which  give  25%  profit  when  sold  at 

a  gain  of  $100? 

In  this  question  :  Then  : 

Gain  =$100.  Gain         _^  $100  ^ 

Rate  of  Gain  =25%,  or  .25.      Rate  of  Gain      "TSS"     ^^'  ^^®  ^^^^^ 

We  have  also  learned  that     Rate  of  Loss  X  Cost  =  Loss. 
From  Wilich 


Loss 


Rate  of  Loss 


=  Cost. 


Application  : 

What  is  the  cost  of  goods  which  show  15%  loss  when  sold  at  a 

loss  of  $30? 

In  this  question  :  Then  : 

Loss  =$30.  Loss  $30 


Rate  of  Loss  =  15%,  or  .15.    Rate  of  Loss      .15 


=  $200,  the  Cost. 


BLACKBOARD  PRACTICE 

What  is  the  cost  of  goods  which  show : 

1.  $75  profit  at  10%?  6.    $30  loss  at  5%? 

2.  $125  profit  at  12%?  7.    $45  loss  at  7^%? 

3.  $250  profit  at  15%?  8.   $67.50  loss  at  6|%? 

4.  $500  profit  at  12|%)?  9.    $125  loss  at  12^%? 
6.   $625  profit  at  16|%?  10.   $250  loss  at  16f%? 


PROFIT  AND  LOSS 


81 


n.   To  Find  the  Rate  of  Gain  When  the  Cost  Price  and  the 
SelUng  Price  are  Known. 

We  have  learned  that     Selling  Price  — Cost  Price  =  Gain. 
And  that  Rale  of  Gain  X  Cost  =  Gain. 

From  the  last  expression, 


Rate  of  Gain  = 


Gain 
Cost 


Application: 

What  is  the  rate  of  gain  when  goods  costing  $60  sell  for  $75  ? 


In  this  question : 
SelUng  Price  =$75 
Cost  Price      =$60 
Gain  =$15 


Then: 
Gain  ^  $15 
Cost      $60 


=  .25  =25%,  Rate  of  Gain. 


in.   To  Find  the  Rate  of  Loss  When  the  Cost  Price  and  the 
SelHng  Price  are  Known. 

We  have  learned  that      Cost  Price  —  Selling  Price  =  Loss. 
And  that  Rate  of  Loss  X  Cost  =  Loss. 

From  the  last  expression, 


Rate  of  Loss 


Loss 
Cost* 


Application  : 

What  is  the  rate  of  loss  when  goods  costing  $120  sell  for  $100? 


In  this  question : 

Cost  Price  =$120 
SeUing  Price  =$100 
Loss  =   $20 


Then 
Loss 


$20 


Cost      $100 


=  .20=20%,  Rate  of  Loss. 


82  PERCENTAGE 

BLACKBOARD  PRACTICE 

Find  the  rate  of  gain  when        Find   the   rate    of   loss    when 
goods  costing  goods  costing 

1.  $300  seU  for  $400.  7.  $300  sell  for  $270. 

2.  $450  sell  for  $540.  8.  $375  sell  for  $300. 

3.  $500  sell  for  $550.  9.  $450  sell  for  $400. 

4.  $500  sell  for  $575.  10.  $600  sell  for  $500. 
6.  $750  sell  for  $1000.  11.  $1200  sell  for  $900. 
6.  $876  sell  for  $1168.  12.  $1800  sell  for  $1500. 

Marking  Goods  with  Private  Cost  Marks. 

Merchants  often  mark  their  goods  with  characters  known  only 
to  the  employees  of  the  firm.  Such  systems  are  based  upon  some 
word  or  words  which  can  be  easily  memorized.     For  example : 

The  letters  of  the  word  r  u  d  i  m  o  n  t  a  1 

may  be  used  for  the  figures      12345  67890. 

Such  a  word  is  called  a  Key.     Using  tliis  key : 

ml     represents  $1.20,  raum  represents  $19,25, 

dnm  "  $3.75,  umll  "  $25.00, 

ell  **  $6.00,  mill  '*  $50.00,  etc. 

Some  firms  use  a  "repeater"  to  help  conceal  their  cost  marks.  If  a 
repeater  "  X  "  is  used,  the  mark  umll  is  wi'itten  umlx. 

If  both  the  cost  price  and  the  selling  price  are  written  on  an  article  or 

a  tag,  it  is  customary  to  Avrite  the  cost  price  over  the  selling  price.     Thus : 

rdm      In  most  cases  merchants  write  the  selling  price  in  plain  figures. 

$1.75* 

Using  the  ke}^  show  how  to  mark  goods  costing : 


1.  $1.00  to  ga 

2.  $1.20  to  ga 

3.  $1.12  to  ga 

4.  $1.25  to  ga 

5.  $1.50  to  ga 

6.  $2.50  to  ga 

7.  $300  to  ga 


n  20%.  8.  $12.50  to  gain  20%. 

n  331%.  9.  $15.00  to  gain  25%. 

n25%.  10.  $18.75  to  gain  20%. 

n  20%,.  11.  $22.50  to  gain  15%. 

n  30%).  12.  $24.00  to  gain  33i%. 

n  30%).  13.  $37.50  to  gain  40%. 

n  16|%.  14.  $50.00  to  gain  37i%. 


EVERYDAY  PROBLEMS  IN  PROFIT  AND  LOSS  83 

WRITTEN  APPLICATIONS 

The  Business  Man's  Problems  in  Profit  and  Loss 

1.  15%  profit  is  gained  on  a  shipment  of  grain  which  cost  a 
dealer  $2400.     How  much  is  his  gain? 

2.  A  shipment  of  grain  which  cost  $2400  was  sold  for  $2670. 
What  is  the  per  cent  of  gain? 

3.  At  the  rate  of  15%  profit  a  dealer  makes  a  profit  of  $360 
on  a  shipment  of  grain.     How  much  did  the  grain  cost  him? 

4.  A  dealer  sold  1700  bushels  of  wheat  at  a  profit  of  15%  and 
received  $1173  for  it.  How  much  did  the  wheat  cost  him  per 
bushel  ? 

5.  A  piece  of  real  estate  which  cost  $4200  increased  16|%  in 
value.     Find  the  amount  of  the  increase  in  value.  '^ 

6.  Lumber  that  cost  $40  per  thousand  is  damaged  5%  and  is 
then  sold  so  as  to  make  a  gain  of  15%  on  its  real  value.  What 
is  the  selling  price  per  thousand  ? 

7.  A  dealer  bought  a  horse  for  $200  and  sold  it  at  a  price 
which  would  give  him  20%  profit .  He  received  only  80%  of  that 
price.  How  much  did  he  lose?  What  per  cent  of  the  cost  did  he 
lose? 

8.  A  merchant  sold  400  collars  at  $.085  each,  and  gained 
25%  by  the  transaction.     How  much  did  he  pay  for  the  coUars  ? 

9.  A  profit  of  80  cents  was  made  on  a  book  that  sold  at  120% 
of  its  cost.     What  was  the  selHng  price  of  the  book? 

10.  A  horse  was  purchased  at  10%  less  than  his  actual  value, 
and  then  sold  at  a  profit  of  15%  more  than  his  value.  ^Tiat  was 
the  gain  per  cent  ? 

11.  A  grocer  bought  sugar  at  9  cents  per  pound,  and  then  sold 
it  all  in  bags  of  5  pounds  each.  What  price  must  he  ask  per  bag 
in  order  to  gain  20%  ? 

12.  A  set  of  books  that  cost  $35  was  sold  for  $43.75.  At  what 
price  must  a  set  costing  $48  be  sold  in  order  to  make  the  same  per 
cent  of  profit? 


84  PERCENTAGE 

13.  A  dealer  marked  a  book  so  as  to  gain  25%  on  its  cost  price, 
but  he  finally  sold  it  for  $3.50,  which  was  a  loss  of  12^%  on  the 
cost.     What  was  the  marked  selling  price  of  the  book? 

14.  A  dealer  bought  coal  at  $8  per  short  ton.  He  sold  it  all 
at  $9  per  short  ton,  and  paid  35  cents  per  ton  for  hauling.  What 
was  the  rate  per  cent  of  his  gain? 

15.  A  farmer  bought  120  acres  of  land  at  $60  an  acre,  and  spent 
$1800  in  improvements.  He  then  sold  the  land  and  the  improve- 
ments and  gained  15%  on  his  total  investment.  How  much  did 
he  receive  per  acre  for  the  property  ? 

16.  50  volumes  of  books  were  sold  at  $2.40  each.  On  one  half 
of  them  the  dealer  gained  20%  of  the  cost  price,  but  on  the  other 
haK  he  lost  20%.     How  much  did  he  gain  or  lose  in  the  transaction  ? 

17.  A  carload  of  ice  cost  $3.90  per  ton,  and  the  freight  charge 
was  3  cents  per  hundredweight.  The  ice  was  sold  at  $0.45  per 
hundredweight.  What  was  the  per  cent  of  profit?  What  was 
the  profit  on  one  thousand  pounds  ? 

18.  A  farm  cost  $7500,  and  40%  of  the  cost  price  was  spent  in 
improvements.  The  farm  was  then  sold  for  $12,600.  Find  the 
amount  of  the  gain  and  the  gain  per  cent  on  the  transaction. 

19.  A  builder  sold  two  houses  for  $4500  each,  gaining  20%  on 
one  of  them  and  losing  20%  on  the  other.  Find  the  cost  price 
of  each  house,  and  the  actual  gain  or  loss  on  the  transaction. 

The  Retail  Merchant's  Method  of  Marking  Goods. 
In  recent  years  large  retailers  have  adopted  the  practice  of 
marking  goods  so  that  the  price  received  shall  return 

(1)  The  cash  cost  of  the  goods  ; 

(2)  The  expenses  of  selling ;  and 

(3)  A  reasonable  percentage  of  profit. 

In  this  classification  the  "  expenses  of  selUng  "  include  such 
items  as  rent,  heat,  light,  clerk  hire,  interest,  insurance,  advertis- 
ing, etc.  (called  overhead  expense). 


MARKING  GOODS 


85 


The  Selling  Price  is  the  Base  in  using  the  Retail  Merchant's 
Method  of  calculating  profits. 

Illustration : 

A  sewing  machine  cost  a  retailer  $18,  and  the  freight  charge 
was  $1.  If  the  retailer  knows  that  his  selling  expense  is  12%, 
at  what  price  shall  he  mark  the  machine  to  gain  a  profit  of  15%  ? 

Let.  the  SeUing  Price  =  100%. 

Reduce  this  price  by  the  selling  cost  and  the  profit  desired. 
Then,  100% -12% -15%  =73%,  the  Wholesale  Cost. 
Also,  $18 +$1  =$19,  the  Cash  Cost. 

We  want  that  number  of  which  $19  is  73%. 
,  Or,  $19  H- .73  =$26.03,  the  Selling  Price.     Result. 

Tables  for  finding  a  Selling  Price  are  readily  obtained,  and 
merchants  save  much  labor  by  using  them.  In  the  following 
table  a  few  cases  are  tabulated  for  convenience : 


9? 

,  Profit  Desired 

%  OP  Sklling- 

EXPENSE 

- 

10 

12 

15 

20 

25 

30 

10 

80 

78 

75 

70 

05 

60 

12 

78 

76 

73 

68 

63 

58 

15 

.  75 

72 

70 

65 

60 

55 

16 

74 

72 

69 

64 

59 

54 

18 

72 

70 

67 

62 

57 

52 

20 

70 

68 

65 

60 

55 

50 

25 

65 

63 

60 

55 

50 

45 

Method  of  Using  the  Table. 

Illustration : 

A  net  profit  of  20%  is  desired  on  goods  costing  in  cash  $2^4,  the 
selling  expense  of  the  business  being  16%.     Find  the  selhng  price. 
Under  "  %  Profit  Desired"  in  column  "20"  and  opposite  "  16"  we  find 


"  64." 


Then  $254  is  64%,  of  the  selling  price. 
Hence,  $254^  .64=$396.87,  the  SelHng  Price. 


Result. 


86  PERCENTAGE 

BLACKBOARD   PRACTICE 

Find  the  selling  price  when  the  cash  cost,  the  per  cent  of  selling 
expense,  and  the  per  cent  of  profit  desired  are,  respectively : 

'1.   $100,  10%,  and  12%.  6.  $1150.50,  18%,  and  20%. 

2.  $100,  15%,  and  12%.  7.  $1875.90,  12%,  and  25%. 

3.  $125,  12%,  and  25%.  8.  $2750.00,  10%,  and  12%. 

4.  $240,  16%,  and  20%.  9.  $10,575.50,  12%,  and  15%. 

5.  $500,  25%,  and  25%.  10.  $24,500.00,  15%,  and  20%. 

11.  A  merchant  bought  furniture  costing  $1500,  and  paid  a 
freight  charge  of  $35.  If  he  estimates  his  selling  expense  at  16%, 
at  what  price  must  he  mark  the  furniture  to  gain  a  profit  of  12%? 

12.  The  freight  on  goods  costing  $2400  was  ^%,  and  the  selling 
expense  was  25%.  At  what  price  did  the  merchant  mark  these 
goods,  if  his  profit  on  them  was  20%? 

13.  A  house  furnisher  paid  $3750  for  a  lot  of  Wilton  rugs,  and 
sold  them  so  that  his  profit  was  15%.  If  the  expense  of  running 
his  business  was  20%,  at  what  price  did  he  sell  his  rugs  to  give 
the  profit  indicated  ? 

COMMERCIAL  DISCOUNT 

Discount  is  the  amount  deducted  from  a  bill  of  goods  or  from 
a  debt. 

Trade  Discount  is  the  discount  made  from  the  published  price 
of  an  article. 

This  form  of  discount  has  its  origin  in  the  constantly  varying 
cost  of  the  materials  and  the  labor  that  enter  into  the  manufactur- 
ing. A  manufacturer  publishes  a  catalogue,  at  a  heavy  expense, 
so  from  time  to  time  he  sends  to  his  customers  a  new  discount  sheet 
to  which  the  customer  refers  in  making  orders.  Thus,  the  chang- 
ing cost  in  manufacturing  is  adjusted  in  fairness  to  both  manu- 
facturer and  retailer  without  the  cost  of  a  new  catalogue. 


DISCOUNT  87 

Cash  Discount  is  the  discount  allowed  for  the  immediate  pay- 
ment of  a  bill. 

Merchandise  is  frequently  offered  to  a  buyer  at  a  reduced  price 
if  payment  for  the  same  is  made  upon  receipt  of  the  goods. 

Time  Discount  is  the  discount  allowed  for  the  payment  of  a 
bill  within  a  specified  time. 

All  three  kinds  of  discount,  trade,  cash,  and  time  discount,  are 
frequently  given  the  general  name,  Commercial  Discounts. 

DIscoimts  are  Reckoned  as  some  rate  per  cent  of  the  amount 
to  be  paid,  or  as  some  fraction  of  the  amount. 

For  example  :  A  10%  discount  on  a  bill  of  $500  means  that  the  amount 
due  is  $500  -  (10%  of  $500)  =$500-150  =$450. 

»    Or,  "yu  ^^"  ^^  ^  ^^^^  ^^  $500  me^ns  that  the  amount  due  is 

$500  -  (yL  of  $500)  =$500  -$50  =$450. 

Fractional  expressions  for  discounts  are  inconvenient  in  cases 
like  8%,  15%,  etc. 

The  Net  Amount  of  a  Bill  is  the  amount  of  the  bill  less  the 
discounts. 

In  the  example  above  the  net  amount  is  $450. 

Business  Practice  in  Commercial  Discount. 

Illustrations : 

A  bill  of  goods,  based  on  catalogue  prices,  amounts  to  $456.50, 
and  the  trade  discount  is  20%.     Find  the  net  amount  of  the  bill. 

Gross  amou  it  of  bill  =  $456.50 

Discount  =20%,  of  $456.50  =$456.50 X. 20  =     91.30 
Net  amount  of  bill  =  $365.20     Result. 

A  bill  of  goods  is  subject  to  a  trade  discoimt  of  30%,  and  an 
additional  cash  discount  of  5%.  If  the  amount  of  the  bill  at  the 
list  price  is  $734.80,  find  the  net  cost  of  the  goods. 

Gross  amount  of  bill  =  $734.80 

Discount  =30%  of  $734.80  =  $734.80 X. 30  =  220.44 

Amount  of  bill  less  trade  discount  =  $514.36 

Cash  discount  =5%  of  $514.36  =$514.36 X. 05  =     25.72 
Net  amount  of  bill  =  $488.64 


1.  $100  at  15%. 

7. 

2.  $125  at  10%. 

8. 

3.  $150  at  20%. 

9. 

4.  $150  at  25%. 

10. 

5.  $260  at  30%. 

11. 

6.  $375  at  40%- 

12. 

88  PERCENTAGE 

BLACKBOARD  PRACTICE 

Find  the  discount  on  a  bill  amounting  to 

$275.50  at  10%. 
$354.20  at  12^%. 
$375.25  at  16|%. 
$465.90  at  33J%. 
$525.75  at  30%. 
$775.40  at  33^%. 

Find  the  net  amount  of  a  bill  of  goods  when  the  list  price  and 
discount  are : 

13.  $27.50  and  10%^.  19.  $54.50  and  12^%. 

14.  $45.90  and  15%.  20.  $75.90  and  15%. 

15.  $96.75  and  12^%o.  21.  $110.50  and  20%). 

16.  $115.10  and  20%.  22.  $250.50  and  25%. 

17.  $175.87  and  25%.  23.  $375.90  and  37^%. 

18.  $290.05  and  30%.  24.  $625.45  and  40%. 

WRITTEN  APPLICATIONS 

The  Business  Man's  Problems  in  Discounts 

1.  Find  the  discount  given  on  a  suit  marked  $24,  if  the  rate 
of  discount  is  20%. 

2.  Find  the  net  price  of  a  suit  marked  $24,  if  the  rate  of  dis- 
count is  20%. 

3.  Find  the  rate  of  discount  when  a  set  of  books  marked  $24 
is  sold  for  $19.20. 

4.  What  is  the  rate  of  discount  when  a  book  marked  $2.00 
is  sold  for  $1.60? 

5.  A  piano  hsted  at  $450  is  sold  at  a  discount  of  10%  for  cash. 
How  much  does  the  dealer  receive  for  it  ? 

6.  Find  the  net  amount  paid  for  25  tons  of  coal  at  $6.40  per 
ton  if  5%  discount  is  allowed  for  cash. 


EVERYDAY  PROBLEMS  IN  DISCOUNTS  89 

7.  A  farmer  bought  a  mowing  machine  at  a  discount  of  16|% 
for  cash.  The  discount  amounted  to  S27.  How  much  did  he 
pay  for  the  machine  ? 

8.  An  auto  truck  is  offered  at  $2750  if  paid  for  in  six  months, 
or  at  $2475  if  paid  for  on  deHve^y^  What  is  the  rate  of  discount 
offered  for  cash? 

9.  A  farmer  bought  a  spraying  outfit  at  a  discount  of  20% 
from  a  list  price  of  $2.60.     What  was  the  cost  of  the  outfit  ? 

10.  What  is  the  net  cost  of  a  bill  of  farming  miplements  amount- 
ing to  $450.90  at  list  prices,  if  the  discount  from  list  prices  is  I%? 

11.  Find  the  selling  price  of  a  sewing  machine  that  was  bought 
at  20%  discount  from  a  list  price  of  $25  and  sold  at  a  profit  of 
40%  on  the  net  cost  price. 

12.  A  farmer  bought  a  potato  planter  listed  at  $83,  and  by 
paying  cash  received  a  discount  of  5%.  The  freight  charge  was 
$1.15.     How  much  did  the  planter  cost  him? 

13.  A  merchant  orders  a  bill  of  goods  at  list  prices  amounting 
to  $1125.  The  discount  on  one  third  of  the  bill  is  15%,  and  on 
the  other  two  thirds  20%.     What  is  the  net  amount  of  the  bill  ? 

14.  A  farmer  paid  $300  for  a  gas  engine.  The  dealer  who  sold 
it  to  him  made  a  profit  of  25%,  and  the  dealer  bought  it  at  a  dis- 
count of  10%  from  the  list  price.  WTiat  was  the  list  price  of  the 
engine  ? 

15.  A  dealer  bought  an  automobile  at  16|%  discount  from 
the  list  price.  The  discount  amounted  to  $240.  The  dealer's 
selling  price  included  the  freight  charges  of  $20,  and  also  a 
profit  of  20%  on  the  net  cost  to  him.  Find  the  selling 
price. 

16.  A  fur  coat  that  cost  a  dealer  $150  was  marked  to  sell  at  a 
profit  of  33§%,  but  it  was  sold  late  in  the  season  at  a  discount  of 
25%  from  the  marked  price.  What  was  the  dealer's  profit  on  the 
coat? 


90  PERCENTAGE 

17.  100  bars  of  soap  are  billed  to  a  grocer  at  $6.25,  and  a  dis- 
count of  20%  is  allowed  him.  What  was  the  cost  per  cake?  If 
the  soap  is  sold  at  10  cents  per  cake,  what  is  the  per  cent  of  profit  ? 

18.  A  dealer  paid  $20  for  a  dozen  hats.  Three  of  them  were 
sold  at  a  profit  of  20%,  but  the  others  were  damaged  by  fire  and 
sold  at  a  loss  of  25%.  How  much  was  the  actual  loss  on  the 
transaction  ? 

19.  A  merchant  is  offered  a  time  discount  of  12^%  on  a  bill 
of  $4800  if  paid  within  30  days,  or  a  cash  discount  of  $640  if  paid 
immediately.  The  merchant  accepts  the  latter  offer.  How  much 
does  he  save  by  the  choice? 

20.  A  dealer  in  books  bought  5000  volumes  at  $1.00  each, 
less  40%.  He  sold  2000  volumes  at  $1.00  each,  1600  at  $.75  each, 
1000  at  50^  each,  and  the  remainder  at  25$!^  each.  How  much 
profit  did  he  make  on  the  whole  lot  ? 

21.  100  sewing  machines  were  bought  at  $22.50  each.  The 
buyer  was  offered  his  choice  of  a  discount  of  10%  for  cash  or  5% 
if  paid  within  30  days.  How  much  did  he  save  by  choosing  the 
better  terms? 

22.  A  merchant  discounted  his  bills  for  a  year,  and  in  that  time 
he  bought  goods  amounting  to  $67,500.  If  the  average  rate  of 
discount  was  5%,  and  if  the  expense  of  running  his  business  was 
15%  of  the  net  cost  of  his  goods,  find  the  amount  he  saved,  and 
the  cost  of  running  his  business. 

23.  Goods  listed  at  $2000  were  bought  at  a  discount  of  15%, 
and  then  sold  at  a  profit  of  20%  on  the  net  cost.  If  the  same 
goods  had  been  bought  at  a  discount  of  20%,  and  then  sold  at  a 
profit  of  30%  on  the  net  cost,  how  much  more  would  the  seller 
have  made  than  in  the  first  case  ? 

24.  A  merchant  received  three  different  bills  of  goods,  the  first 
for  $1180  with  10%  discount  for  cash,  the  second  for  $750  with 
20%  trade  discount,  and  the  third  for  $960  with  12|%o  trade  dis- 
count and  5%  for  cash.  Find  the  total  net  amount  of  all  three 
bills. 


DISCOUNT  SERIES  91 

Discount  Series. 

In  many  business  transactions  it  is  impossible  for  a  manufac- 
turer to  publish  a  discount  sheet  by  which  he  agrees  to  bind  him- 
self for  any  length  of  time,  for  the  changes  in  manufacturing  costs 
often  come  unexpectedly.  For  example,  a  manufacturer  of  rugs 
may  have  pubUshed  a  price  list  in  which  he  offers  his  product  at 
a  discount  of  10%,  when  he  is  suddenly  confronted  with  the  need 
for  making  further  discounts  or  lose  valuable  business  to  a  com- 
peting manufacturer.  To  meet  the  competition  he  gives  notice 
to  his  customers  of  an  additional  discount,  and  sends  his  bills  out 
with  the  original  10%  reduction,  and  an  additional  5%.  On 
such  a  bill  he  gives,  therefore,  10%  and  5%,  and  the  commercial 
expression  Ls  either  "  with  10%  and  5%  off,"  or  "  less  10  and  5." 

Two  or  more  discounts  allowed  on  a  bill  are  called  Discount 
Series. 

Illustration : 

A  bill  of  goods  amounting  to  S2450  is  sold  subject  to  discounts 
of  20%,  10%,  and  5%.     Find  the  net  amount  of  the  bill. 

20%  of  $2450  =  $490.  $2450  -  $490  =  $1960. 

10%  of  $1960  =$196.  $1960 -$196  =$1764. 

5%  of  $1764  =$88.20.  $1764 -$88.20  =$1675.80.     Result. 

The  first  discount  is  from  the  list  price. 
The  second  discount  is  from  the  first  remainder. 
The  third  discount  is  from  the  second  remainder,  etc. 

BLACKBOARD   PRACTICE 

From  the  following  amounts  obtain  the  net  amounts  at  the 
discounts  indicated. 

1.  $75  at  10%  and  5%.  6.  $350  at  15%,  10%,  and  5%. 

2.  $90  at  10%o  and  5%.  7.  $400  at  10%,  8%,  and  5%. 

3.  $100  at  20%)  and  10%).  8.  $575  at  20%,  8%,  and  5%. 

4.  $125  at  20%o  and  15%.  9.  $790  at  10%,  10%,  and  10%. 

5.  $150  at  25%  and  20%.  10.  $950  at  25%,  20%,  and  10%. 


92  PERCENTAGE 

WRITTEN  APPLICATIONS 

1.  Find  the  net  cost  of  a  piano  listed  at  $600,  with  discounts 
of  20%  and  10%. 

2.  Find  the  net  cost  of  a  bill  of  dry  goods  amounting  to  $240 
at  list  prices  with  discounts  of  20%,  15%,  and  10%. 

3.  If  a  dealer  buys  a  sewing  machine  at  discounts  of  20% 
and  10%  from  the  list  price,  and  then  sells  it  at  the  list  price, 
what  is  his  per  cent  of  profit? 

4.  The  list  price  of  a  cultivator  was  $18  and  a  dealer  bought 
it  at  discounts  of  10%  and  5%  from  the  list  price,  and  sold  it  for 
$20.     How  much  was  his  profit  ? 

5.  A  firm  hsted  a  set  of  books  at  $90,  less  20%  and  10%. 
Another  firm  listed  the  same  set  of  books  at  $90,  less  15%  and 
15%.     Which  is  the  better  offer? 

6.  Goods  amounting  to  $1500  at  list  prices  are  bought  by  a 
wholesaler  at  discounts  of  10%  and  5%.  He  sells  them  at  8% 
and  2%  from  the  same  list  prices.     How  much  does  he  gain? 

7.  Discounts  of  15%,  10%,  and  5%  are  allowed  on  a  bill  of 
goods  amounting  to  $1200.  Would  the  discount  be  greater  or  less 
if  5%,  10%,  and  15%  were  allowed  instead? 

8.  A  piano  is  listed  at  $750  with  discounts  of  20%  and  20%. 
If  the  dealer  sells  it  for  $600,  what  is  the  per  cent  of  his  profit  ? 

9.  A  firm  offers  a  machine  at  25%  off  from  a  Hst  price  of  $275. 
A  rival  firm's  discounts  from  the  same  list  price  for  the  same 
machine  are  15%,  10%,  and  5%.     WTiich  is  the  better  offer? 

10.  Ten  sewing  machines  listed  at  $45  each  are  sold  at  20  and 
10  off.  The  buyer  then  sold  them  all  at  a  profit  of  25%.  W'lat 
was  his  net  gain  on  all  of  them  ? 

11.  An  agent  for  farm  implements  bought  a  250-gallon  sprayer 
listed  at  $250,  and  was  given  discounts  of  20%  and  5%.  He 
sold  the  sprayer  to  a  farmer  at  a  profit  of  20%  less  5%  discount 
for  cash.  How  much  did  the  agent  make  on  the  sale?  What  did 
the  farmer  pay  for  the  sprayer? 


BILLS  AND  DISCOUNTS 


93 


Application  of  Discounts  to  Bills. 

The  following  bill  illustratos  modern  business  practice  in  bills 
and  discounts : 


PMH  Ann  PMiA  \Myy^^     iq/^ 

PILLSBURY  FURNITURE  CO. 

DEALERS     IN 

Fine  Furniture,  Rugs  and  Draperies 


Sold  to. 


A 


\yt^^L^ 


/Z,7\ 


/^/jT  ZS 


CO 


S'o 


Sometimes  the  different  items  in  a  bill  of  merchandise  are  sub- 
ject to  discounts  at  different  rates.  In  such  cases  the  discount  on 
each  item  must  be  deducted  separately,  and  the  total  net  amount 
of  the  bill  is  the  sum  of  the  net  amounts  charged  for  the  different 
items. 

WRITTEN   APPLICATIONS 

In  each  of  the  following  exercises  make  out  a  bill,  taking  care 
to  rule  a  sheet  so  that  it  is  an  exact  copy  of  a  modern  bill-head. 
In  all  such  work  you  must  continually  strive  for 

1.  Accuracy. 

2.  Clearness. 

3.  Neatness. 


94  PERCENTAGE 

1.  J.  M.  French  bought  of  the  Great  Northern  Furniture 
Company,  12  dinmg  room  tables  at  $16.50  apiece ;  36  chairs  at 
$2.25  apiece;  15  couches  at  $10.75  apiece;  18  morris  chairs  at 
$10.25  apiece.  Terms,  15%  and  10%.  Find  the  net  amount 
of  the  bill. 

2.  WilUam  L.  Earle  &  Co.  bought  of  the  Sunset  Fruit  Com- 
pany, 100  cases  lemons  at  $4.25  per  case;  60  cases  oranges  at 
$5.60  per  case;  200  bunches  bananas  at  $1.35  per  bunch;  30 
dozen  pineapples  at  $1.20  per  dozen.  Terms,  20%  and  12^%. 
Find  net  amount  of  bill. 

3.  Gibson  &  Wheeler  bought  of  the  Whitman  Carpet  Co., 
200  yd.  Brussels  carpet  at  $1.80  per  yard ;  300  yd.  ingrain  carpet 
at  $1.40  per  yard;  145  8' 3"  X 10' 6''  rugs  at  $20  apiece;  and 
80  6'X9'  rugs  at  $14  apiece.  Terms,  25%  and  5%.  Find  the 
net  amount  of  the  bill. 

4.  Mitchell  &  Hallman  bought  of  Kent  &  Eraser,  dealers  in 
Men's  Furnishings,  15  dozen  ties  at  $4.25  per  dozen;  3  dozen 
ties  at  $12.00  per  dozen  ;  4  dozen  ties  at  $15.00  per  dozen ;  6  dozen 
gloves  at  $15.00  per  dozen ;  18  dozen  gloves  at  $12.25  per  dozen ; 
35  dozen  leather  belts  at  $8.00  per  dozen ;  5  gross  handkerchiefs 
at  $10.50  per  gross.  Terms,  10%  and  5%.  Find  the  net  amount 
of  the  bill. 

5.  The  Glenwood  Hardware  Company  bought  of  the  French 
Manufacturing  Company,  5  dozen  shovels  at  $7.50  per  dozen ; 
10  dozen  iron  rakes  at  $2.60  per  dozen ;  25  dozen  scythes  at  $6.25 
per  dozen;  10  dozen  scythe  snaths  at  $8.00  per  dozen;  4  dozen 
jack  planes  at  $9.00  per  dozen  ;  5  dozen  smoothing  planes  at  $7.50 
per  dozen  ;  24  dozen  chisels  at  $6.10  per  dozen  ;  12  dozen  hammers 
at  $4.50  per  dozen;  8  dozen  screwdrivers  at  $3.25  per  dozen; 
5  dozen  cross-cut  saws  at  $8.50  per  dozen ;  3  dozen  back  saws  at 
$9.50  per  dozen;  and  4  dozen  braces  at  $9.00  per  dozen.  This 
bill  was  sold  at  net  list  prices,  with  2%  off  for  cash.  Find  the 
amount  of  the  bill  if  the  buyer  took  advantage  of  the  cash 
discount. 


INTEREST  95 

INTEREST 

Interest  is  money  paid  for  the  use  of  money. 

If  you  borrow  $1000,  and  repay  the  loan  at  the  end  of  1  year,  and  if 
you  pay  $60  for  the  use  of  the  money,  the  $60  is  called  Interest. 

The  Principal  is  the  money  on  which  interest  is  paid. 

In  the  illustration  $1000  is  the  principal. 

the  Time  is  the  period  for  which  the  money  is  borrowed  or 
loaned. 

In  the  illustration  1  year  is  the  time. 

The  Rate  of  Interest,  or  the  Rate,  is  the  number  of  hundredths 
of  the  principal  paid  as  interest  for  one  year. 

In  the  illustration  $60  is  paid  for  the  use  of  $1000. 
What  decimal  part  of  $1000  is  $60  ? 

$60    _    6    _ 
SIOOO      100 

But,  expressed  as  a  per  cent,  .06  =6%. 

That  is,  the  rate  of  interest  in  the  illustration  is  6%. 

Simple  Interest  is  interest  charged  only  on  the  principal.  In 
this  book  the  word  "  interest  "  used  alone  will  always  mean  simple 
interest. 

Problems  in  interest  are  really  problems  in  percentage  with 
the  element  of  time  added.     In  a  problem  in  interest 

The  Principal  =  The  Base 

The  Rate  =  The  Rate  Per  Cent 
The  Interest  =  The  Percentage 

Several  methods  for  computing  interest  are  in  common  use,  and 
it  is  difficult  to  give  a  single  process  that  will  meet  all  needs.  The 
following  methods  are  all  practical,  and  you  should  master  the 
one  based  upon  a  principal  of  one  dollar,  and  the  method  of 
'^  Exact  Interest." 


96  INTEREST 

METHODS   OF  FINDING   INTEREST 
I.  When  the  Time  is  Given  in  Years,  Months,  and  Days 

Illustrations : 

1.  Find  the  interest  on  $900  for  3  years  at  5%. 

The  interest  for  1  year  at  5%  =.05  X$900  =$45.00. 

The  interest  for  3  years  at  5%  =3  X $45.00  =$135.00.     Result. 

2.  Find  the  interest  on  $900  for  3  years  5  months  at  6%. 

Expressed  in  years  the  time  =  3^^  years. 

The  interest  on  $900  for  1  year  at  6%  =.06 X $900  =$54.00. 

The  interest  on  $900  for  3 j\  years  =  3fV  X $54.00  =  $184.50.     Result 

3.  Find  the  interest  on  $1200  for  4  years  3  months  12  days  at 

3%. 

The  time  expressed  in  years  =4^  years. 

The  interest  on  $1200  for  1  year  =  .05  X  $1200  =$60.00.  ' 

The  interest  on  $1200  for  4^  years  =4iJ  X$60  =  $257.00.     Result. 

For  a  general  expression  of  the  process  just  illustrated  we  have 

Multiply  the  principal  by  the  rate. 

Multiply  the  product  hy  the  time  expressed  in  years. 

BLACKBOARD  PRACTICE 

With  the  principal,  the  time,  and  the  rate,  as  follows,  find  the 
interest  on : 

1.  $1000  for  4  yr.  at  5%.  4.    $125.50  for  3  yr.  at  5%. 

2.  $1200  for  3  yr.  at  6%.  5.   $225.75  for  5  yr.  at  4%. 

3.  $1750  for  5  yr.  at  ^%.  6.   $457.25  for  4  yr.  at  5.4%. 

7.  $700  for  2  yr.  6  mo.  at  6%. 

8.  $1400  for  3  yr.  3  mo.  at  3%. 

9.  $2100  for  4  yr.  10  mo.  at  4%. 

10.  $135.80  for  3  yr.  4  mo.  at  5%. 

11.  $457.75  for  22  yr.  7  mo.  at  4%. 

12.  $675.50  for  4  yr.  5  mo.  at  5%. 

13.  $300  for  2  yr.  6  mo.  15  da.  at  4%. 


THE  SIX  PER  CENT  METHOD  97 

14.  $450  for  3  yr.  8  mo.  18  da.  at  5%. 

15.  $600  for  5  yr.  3  mo.  6  da.  at  4^%. 

16.  $900  for  2  yr.  2  mo.  3  da.  at  4^%. 

17.  $1250  for  3  yr.  11  mo.  24  da.  at  5%. 

18.  $1800  for  2  yr.  9  mo.  20  da.  at  5%. 

19.  $2500  for  3  yr.  7  mo.  25  da.  at  6%. 

n.   Interest  Based  upon  a  Principal  of  One  Dollar 

The  value  of  this  method  lies  in  the  ease  with  which  we  may 
compute  the  interest  on  $1  for  any  given  time  at  6%. 

1  month  =  ^2  year, 
6  days  =  J  month, 
1  day  =  ^  of  ^  month,  =  -^^  month. 
Then: 

The  interest  on  $1  for  1  year  at  6%  =  $.06. 
The  interest  on  $1  for  1  month  at  6%  =  $.005. 
The  interest  on  $1  for  6  days  at  6%  =  $.001. 
The  interest  on  $1  for  1  day  at  6%  =  $.000i. 
These  units  multiplied  by  the  given  time  expressed  in  years, 
months,  and  days,  give  the  interest  on  $1  for  that  time  at  6%. 

Illustrations : 

1.  Find  the  interest  on  $250  for  3  yr.  5  mo.  12  da.  at  6%. 

Interest  on  $1  for  3  years  at  6%  =3  XS.06  =  $.18 

Interest  on  $1  for  5  months  at  6%  =5  XS.OOo  =  .025 

Interest  on  $1  for  12  days  at  6%  =  12 X$.000^  =  .002 

Interest  on  $1  for  3  years  5  months  12  days  at  6%  =$.207 
Interest  on  $250  for  3  yr.  5  mo.  12  da.  =250  X $.207  =$51.75.     Result. 

2.  Find  the  interest  on  $625.40  for  4  yr.  7  mo.  19  da.  at  6%. 

Interest  on  $1  for  4  years  at  6%  =  $.24. 

Interest  on  $1  for  7  months  at  6%  =  $.035. 

Interest  on  $1  for  19  days  at  6%  =  $.003^. 

Interest  on  $1  for  4  yr.  7  mo.  19  da.  at  6%  =  $.278^. 
Interest  on  $625.40  for  4  years  7  months  19  days  at  6%  =  .278ix$625.40 
=  $173.96543  or,  $173.97.     Result. 


98  •  INTEREST 

3.    Find  the  interest  on  $450  from  June  10,  1916,  to  April  28, 
1919,  at  6%. 

:yr.        mo.     da. 

The  time  between  the  two  dates  is  found  by  subtraction      1919       4     28 
as  indicated  at  the  right.  1916       6     10 

2     10     18 
That  is,  the  time  is  2  years  10  months  18  days. 
Interest  on  $1  for  2  years  at  6%  =       $.12  $450 

Interest  on  $1  for  10  months  at  6%  =    .05  .173 

Interest  on  $1  for  18  days  at  6%  =         .003  1350 

Interest  for  the  whole  time  at  6%  =    $.173  3150 

450 


$77,850     Result, 
BLACKBOARD  PRACTICE 

Find  the  interest  on  : 

1  $150  for  2  yr.  5  mo.  12  da.  at  6%. 

2  $225  for  2  yr.  9  mo.  18  da.  at  6%. 

3.  $290.50  for  3  yr.  8  mo.  24  da.  at  6%. 

4.  $210.50  for  2  yr.  10  mo.  6  da.  at  6%. 

5.  $342.12  for  3  yr.  7  mo.  15  da.  at  6%. 

6.  $497.18  for  2  yr.  8  mo.  17  da.  at  6%. 

7.  $654.32  for  3  yr.  5  mo.  25  da.  at  6%. 

8.  $872.19  for  3  yr.  7  mo.  17  da.  at  6%. 

9.  $1024.17  for  3  yr.  11  mo.  5  da.  at  6%. 

10.  $3512.19  for  1  yr.  1  mo.  19  da.  at  6%. 

11.  $4647.20  for  2  yr.  10  mo.  27  da.  at  6%. 

12.  $869.15  for  1  yr.  8  mo.  26  da.  at  6%. 

13.  $250  from  January  1,  1918,  to  March  1,  1919,  at  6%. 

14.  $375  from  April  1,  1917,  to  July  1,  1919,  at  6%. 

15.  $500  from  March  10,  1916,  to  May  16,  1918,  at  6%. 

16.  $275.50  from  June  1,  1918,  to  July  19,  1919,  at  6%. 

17.  $457.80  from  October  1,  1917,  to  January  10,  1920,  at  6%. 

18.  $625.50  from  March  1,  1916,  to  October  16,  1919,  at  6%. 

19.  $1275  from  April  11,  1915,  to  January  25,  1919,  at  6%. 


CHANGING  A  RESULT  99 

20.  $2500  from  June  11,  1918,  to  July  29,  1919,  at  6%. 

21.  $3000  from  September  11,  1917,  to  June  30,  1918,  at  6%. 

22.  $5400  from  September  11,  1916,  to  January  19,  1920,  at  6%. 

To  Change  a  Result  Obtained  at  6%  to  a  Result  at  Any  Other 
Given  Rate. 

The  method  just  illustrated  depends  wholly  upon  a  calcula- 
tion at  6%,  hence  it  is  necessary  to  learn  a  method  whereby  a 
result  may  be  changed  to  a  rate  other  than  6%.  The  change  is 
readily  made  by  a  simple  operation  in  division  with  either  addition 
or  subtraction. 

Illustrations : 

Find  the  interest  on  $1200  for  1  yr.  5  mo.  10  da.  at  7%. 

By  the  method  just  learned : 

Interest  on  $1200  for  1  yr.  5  mo.  10  da.  at  6%  =  $104.00 

Now7%=6%+iof  6%=6%  +  l%. 
Then,  since  $104  =  interest  at  6%, 
the  interest  at  1  %  =  $104  ^  6  =  17.33 

Adding,  interest  at  7%=  $121.33      Result. 

Interest  at  the  rates  most  commonly  used  may  be  found  readily 
from  6%  results  as  follows : 

For  interest  at  3%  Divide  interest  at  6%  by  2. 

For  interest  at  4%  Subtract  ^  of  interest  at  6%. 

For  interest  at  4^%  Subtract  ^  of  interest  at  6%. 

For  interest  at  5%  Subtract  -i-  of  interest  at  6%. 

For  interest  at  5^%  Subtract  -^  of  interest  at  6%. 

For  interest  at  7%  Add  ^  of  interest  at  6%. 

In  Pennsylvania  many  interest  contracts  are  made  at  a  rate 
of  5.4%. 

5.4%  =  ^  of  6%  =  .9  of  6%. 
Therefore,  for  interest  at  5.4%,  multiply  interest  at  6%  by  .d. 


100  INTEREST 

BLACKBOARD   PRACTICE 

Change  the  following  6%  results  to  results  at  the  indicated  rate : 


To  3% : 

To  4% : 

To  5%  : 

To  7% : 

1.    $274.60. 

5.    $450.60. 

9.    $327.30. 

13.    $320.16. 

2.    $342.16. 

6.    $542.10. 

10.    $343.17. 

14.    $384.42. 

3.    $454.48. 

7.    $642.12. 

11.    $460.10. 

15.    $428.11. 

4.    $564.29. 

8.    $746.19. 

12.    $574.70. 

16.    $542.19. 

To  4i% : 

To  5i% : 

To  5.4%  : 

To  6i% : 

17.    $64.96. 

21.    $120.60. 

25.    $110.19. 

29.    $627.12. 

18.    $72.48. 

22.    $248.40. 

26.    $370.12. 

30.    $518.28. 

19.   $68.76. 

23.    $436.08. 

27.    $340.16. 

31.    $642.10. 

20.    $85.19. 

24.    $511.19. 

28.    $510.17. 

32.    $754.09. 

The  Amount  is  the  sum  of  the  principal  and  the  interest. 
If  $1000  is  loaned  at  6%  for  3  yr.  the  interest  is  $180. 
$1000+$180  =  $1180,  the  amount  due  at  the  end  of  the  third 
year. 

III.   When  the  Time  is  Included  between  Two  Given  Dates 

The  two  methods  that  follow  are  of  great  practical  value  when 
the  interest  period  is  short,  particularly  when  the  time  is  less 
than  one  year.  Both  methods  are  extremely  accurate,  and  the 
first  is  known  as 

(a)  The  Method  of  Exact  Interest. 

Illustration : 

Fmd  the  interest  on  $450  from  Nov.  12,  1918,  to  March  19, 
1919,  at  6%. 

Counting  the  exact  number  of  days  between  the  two  dates,  we  have 
Nov.  (18)+Dec.  (31)+ Jan.  (31)+Feb.  (28) +March  (19)  =127  days. 
Then,  ifl-  X  6  %  of  $450  =  the  required  interest. 

Tj  11  ^-  127X6X450     ^  -^. 

By  cancellation  :    — ^^^tttk^t^  =9.12+ 

3d5  X 100 

Therefore,  the  required  interest  =$9.12.     Result, 


>         at        >      a 


METHOD  OF  EXACT  INTEREST  101 


This  method  is  used  by  the  United  States  Government  and  by 
many  of  the  leading  trust  companies.  It  is  also  the  method  used 
by  many  of  the  states  in  their  financial  problems. 

BLACKBOARD  PRACTICE 
Find  the  exact  interest  on 

1.  $200  for  48  da.  at  5%.  6.  $425  for  82  da.  at  6%. 

2.  $300  for  38  da.  at  5%.  7.  $570  for  70  da.  at  5^%. 

3.  $325  for  57  da.  at  6%.  8.  $625  for  87  da.  at  4^%. 

4.  $275  for  72  da.  at  6%.  9.  $750  for  112  da.  at  5.4%. 

5.  $425  for  69  da.  at  5%.  10.  $875  for  164  da.  at  6%. 

11.  $235  from  April  7  to  June  12  at  6%. 

12.  $345  from  May  10  to  October  16  at  5%. 

13.  $457  from  June  3  to  August  12  at  6%. 

14.  $125.60  from  March  11  to  September  20  at  5%. 

15.  $175.90  from  April  17  to  December  19  at  6%. 

16.  $240.24  from  May  9  to  December  31  at  6%. 

17.  $275.37  from  October  10  to  March  17  at  5^%. 

18.  $310.79  from  August  13  to  Januarys  17  at  6%. 

19.  $427.52  from  September  19  to  Februarys  5  at  5.4%. 

20.  $510.43  from  December  30  to  May  9  at  6%. 

21.  $570.64  from  July  12  to  January  19  at  6%. 

22.  $627.45  from  April  15  to  March  14  at  5%. 

23.  $895.56  from  May  23  to  February  4  at  6%. 

24.  $900.00  from  July  19  to  October  27  at  5%. 

25.  $975.50  from  November  19  to  March  28  at  6%. 

26.  $1000.00  from  December  18  to  September  18  at  6%. 

27.  $1125  from  January  19  to  August  17  at  5%. 

28.  $1240.12  from  February  17  to  January  11  at  5^%,. 


1 02  INTEREST 

(6)  The  ''  Banker's  Time  ''  Method. 

Bankers  often  calculate  time  by  months  and  days,  using  the 
number  of  months  and  the  exact  number  of  days  for  the  fractional 
part  of  the  month  in  the  given  time. 

Illustration : 

Find  the  interest  on  $450  from  Sept.  12,  1917,  to  June  19,  1918, 

at  6%. 

From  September  12  to  June  12  is  9  months. 

From  June  12  to  June  19  is  7  days.     Hence,  the  time  is  9  mo.  7  da. 

Interest  on  $1  for  9  mo.  at  6%  =  $.045 

Interest  on  $1  tor  7  da.  at  6%  =  .001^ 

Interest  on  $1  for  9  mo.  7  da.  at  6%  =$^461^ 
Then,  .046^ X$450  =$20,775,  or  $20.78.     Result. 

BLACKBOARD   PRACTICE 

Using  ''  Banker's  Time  "  method  and  a  rate  of  6%,  find  the 
interest  on  : 

1.  $150  from  July  10  to  October  8. 

2.  $200  from  May  7  to  August  15. 

3.  $375  from  February  9  to  June  17. 

4.  $450  from  April  17  to  October  11. 

5.  $625  from  June  10  to  December  20. 

6.  $750  from  October  11  to  February  20. 

7.  $925  from  January  11  to  October  15. 

8.  $1100  from  May  15  to  December  18. 

9.  $1500  from  August  11  to  January  19. 

10.  $1650  from  November  18  to  May  11. 

11.  $1875  from  January  31  to  October  9. 

12.  $1576.50  from  December  18  to  February  10. 

13.  $3750.25  from  May  11  to  June  5. 

14.  $5500  from  December  30  to  February  28. 

15.  $8500  from  October  18  to  December  31. 


USING  THE   INTEREST  TABLE 


103 


rV.   Interest  Calculated  from  the  Interest  Table 

For  the  use  of  bankers  and  business  men  whose  work  requires 
frequent  calculations  of  interest,  there  are  published  complete 
tables  from  which  the  interest  on  any  amount  for  any  given  time 
may  be  rapidly  calculated.  The  following  are  incomplete  portions 
of  a  page  from  one  of  the  standard  tables  in  common  use.  The 
table  illustrated  is  based  upon  360  days  to  the  year,  and  a  rate 
of  6%. 


Years 

$1000 

S2000 

$3000 

$4000 

$5000 

$6000 

$7000 

$8000 

$9000 

1 

60 

120 

180 

240 

300 

360 

420 

480 

540 

2 

120 

240 

360 

480 

600 

720 

840 

960 

1080 

3 

180 

360 



540 

720 

900 

1080 

1260 

1440 

1620 

Months 

siooo 

$2000 

$3000 

$4000 

$5000 

$6000 

$7000 

$8000 

$9000 

1 

5 

10 

15 

20 

25 

30 

35 

40 

45 

2 

10 

20 

30 

40 

50 

60 

70 

80 

90 

3 

15 

30 

45 

60 

75 

90 

105 

120 

135 

Days 

SIOOO 

$2000 

S3000 

$4000 

$5000 

$6000 

$7000 

^000 

$9000 

1 

.167 

.333 

.50 

.667 

.833 

1.00 

1.167 

1.333 

1.50 

2 

.333 

.667 

1.00 

1.333 

1.667 

2.00 

2.333 

2.667 

43.00 

3 

.500 

1.000 

1.50 

2.000 

2.500 

3.00 

3.500 

4.000 

.50 

4 

.667 

1.333 

2.00 

2.667 

3.333 

4.00 

4.667 

5.333 

6.00 

5 

.833 

1.667 

2.50 

3.333 

4.167 

5.00 

5.833 

6.667 

7.50 

6 

1.000 

2.000 

3.00 

4.000 

5.000 

6.00 

7.000 

8.000 

9.00 

7 

1.167 

2.333 

3.50 

4.667 

5.833 

7.00 

8.167 

9.333 

10.50 

8 

1.333 

2.667 

4.00 

5.333 

6.667 

8.00 

9.333 

10.667 

12.00 

In  this  table  the  totals  are  based  upon  a  principal  of  $1000. 
For  hundreds  and  tens  of  dollars,  therefore,  we  may  take  decimal 
parts  of  the  totals  given,  remembering  that 

$100  is  .1  of  $1000. 
$10  is  .01  of  $1000,  etc. 

After  finding  the  required  interest  at  6%  by  use  of  the  table, 
the  result  may  be  changed  to  any  other  rate  as  already  shown. 


104  INTEREST 

Illustration : 

Find  the  interest  on  $3250  for  3  yr.  3  mo.  8  da.  at  6%. 

The  following  form  is  convenient : 

3  yr.  3  mo.  8  da. 

Interest  on  $3000  =  $540     $45  $4 

Interest  on    $200=     36         3  .267 

Interest  on      $50  = 9     ^         .067 

Interest  on  $3250  =$585 +$48.75 +$4,334  =$638.08.     Result. 

BLACKBOARD  PRACTICE 

Using  the  table,  find  the  interest  on 

1.  $150  for  2  yr.  at  6%.  6.  $450  for  2  yr.  7  mo.  at  6%. 

2.  $275  for  3  yr.  at  6%.  7.  $625  for  3  yr.  5  mo.  at  5%. 

3.  $400  for  3  yr.  at  6%.  8.  $750  for  3  yr.  2  mo.  at  7%. 

4.  $550  for  4  yr.  at  5%.  9.  $900  for  3  yr.  5  mo.  at  5^%. 

5.  $750  for  4  yr.  at  7%.  10.  $1250  for  2  yr.  5  mo.  at  6%. 

11.  $1225  for  2  yr.  5  mo.  10  da.  at  5%. 

12.  $2345  for  3  yr.  6  mo.  5  da.  at  6%. 

13.  $3550  for  3  yr.  5  mo.  3  da.  at  6%. 

14.  $4575  for  3  yr.  5  mo.  5  da.  at  5%. 

15.  $5870  for  3  yr.  6  mo.  15  da.  at  6%. 

16.  Find  the  interest  on  $450  from  January  10  to  September  10 
at  6%. 

17.  Find  the  interest  on  $1200  from  March  11  to  August  19 

at  5%. 

18.  Find  the  interest  on  $6000  from  November  10,  1915,  to 
September  12,  1916,  at  5%. 

19.  A  note  for  $250  is  given  on  March  12,  1918,  for  six  months, 
and  is  renewed  on  September  12  for  six  months  longer.  Find  the 
interest  for  the  whole  time  at  6%. 

20.  Two  notes  for  $500  each  are  given  on  May  1,  1918.  One  is 
due  March  3,  and  the  other  June  1,  1919.  Find  the  total  amount 
of  both  notes,  the  interest  rate  being  5%. 


SAVING   AND   INVESTING   :M0NEY 

I.    Savings  Bank 

A  Savings  Bank  is  an  institution  that  receives  and  safeguards 
the  savings  of  individuals,  paying  them  a  stated  rate  of  interest 
for  the  use  of  their  money. 

Savings  Banks  are  under  the  rigid  control  of  the  State  Gov- 
ernments. 

Savings  in  the  United  States.  The  growth  of  the  savings  banks 
in  the  United  States  is  an  interesting  study.  In  1850  there  were 
108  savings  banks  in  this  country,  and  251,354  depositors  had  to 
their  credit  a  total  of  $43,431,130.  In  1918  there  were  1819  sav- 
ings banks  and  11,379,553  depositors  had  to  their  credit  a  total 
of  $5,471,579,948.  The  average  amount  on  deposit  per  person  in 
1850  was  $172.78,  but  in  1918  this  average  had  grown  to  $480.82. 

Interest  on  Deposits.  Most  savings  banks  compute  interest 
twice  each  year,  usually  on  January  1  and  July  1.  The  depositor 
may  withdraw  his  interest,  but  if  he  does  not  withdraw  it,  the 
bank  credits  it  to  his  account. 

While  the  custom  varies,  most  savings  banks  designate  certain 
periods  in  which  deposits  begin  to  draw  interest.  In  such  cases 
deposits  made  after  fixed  dates  do  not  begin  to  draw  interest  until 
the  beginning  of  the  next  stated  period.  For  purpose  of  illus- 
trating, the  exercises  that  follow  are  based  upon  the  following 
dates : 

Deposits  made  Draw  Interest 

From  Jan.  1  to  Jan.  15,  From  Jan.  1. 

From  Jan.  16  to  Apr.  1,  From  Apr.  1. 

From  July  1  to  July  15,  From  July  1. 

From  July  16  to  Oct.  1,  From  Oct.  1. 

105 


106  SAVING  AND  INVESTING  MONEY 

How  Savings  Banks  Calculate  Interest. 

Illustration : 

On  July  1,  Donald  deposited  $10  in  a  savings  bank;  on  Sep- 
tember 20,  $30 ;  and  on  November  5,  $20.  Find  his  total  credit 
on  April  1,  if  the  bank  pays  4%,  and  credits  interest  on  January  1 
and  July  1,  if  interest  is  allowed  as  indicated  below. 

July  1,  Deposit $10.00 

Interest  on  $10,  to  Jan.  1 .20 

Sept.  20,  Deposit 30.00 

Interest  on  $30,  to  Jan.  1 .30 

Nov.  5,  Deposit 20.00 

(No  interest  allowed.     See  note.) .00 

Amount  on  deposit,  Jan.  1 60.50 

Interest  on  $60  to  April  1 60 

Amount  of  deposit,  April  1 61.10 

The  deposit  of  $20  in  November  having  been  made  after  Oct.  1,  does 
not  begin  to  bear  interest  until  Jan.  1,  hence  no  interest  was  allowed. 
Savings  banks  usually  disregard  the  cents  when  calculating  interest; 
thus,  if  a  total  deposit  is  $125.19,  they  calculate  interest  on  $125. 

WRITTEN  APPLICATIONS 

1.  A  deposit  of  $200  was  made  in  a  savings  bank  on  January  1, 
1918.  If  the  bank  credits  interest  on  July  1  and  January  1,  find 
the  amount  of  this  deposit  Jan.  1,  1919,  the  rate  being  4%. 

2.  A  deposit  of  $350  was  made  in  a  savings  bank  on  Jan.  1,  1916. 
If  the  bank  credits  interest  on  April  1,  July  1,  October  1,  and 
January  1,  find  the  amount  of  this  deposit  on  Jan.  1,  1917,  the 
rate  being  4%. 

3.  If,  in  the  bank  mentioned  in  example  2,  a  deposit  of  $100 
is  made  on  each  of  the  days  on  which  interest  is  credited,  find  the 
amount  to  the  credit  of  the  depositor  on  Jan.  1,  1917,  the  first 
deposit  having  been  made  on  Apr.  1,  1916. 

4.  $1000  is  deposited  in  a  bank  paying  3%  on  Jan.  1,  1916. 
$400  is  withdrawn  on  July  2.  Find  the  amount  to  the  credit  of 
the  depositor  on  Jan.  1,  1917,  if  the  bank  calculates  and  credits 
its  interest  only  semi-annually. 


LIBERTY  LOAN  BONDS  107 

II.    The  Liberty  Loan  Bonds 

A  Bond  is  a  formal  written  promise  to  pay  a  specified  sum  at  a 
given  time. 

The  Liberty  Loan  Bonds  are  United  States  Government  Bonds, 
and  include  four  issues. 

The  First  Liberty  Loan  bears  interest  at  3-2-%  and  is  due  June  15,  1947. 

The  Second  Liberty  Loan  bears  interest  at  4%  and  is  due  November 
15,  1942. 

The  Third  Liberty  Loan  bears  interest  at  4-i-%  and  is  due  September 
15,  1928. 

The  Fourth  Liberty  Loan  bears  interest  at  4^%  and  is  due  October  15, 
1938. 

The  Victory  Loan  bears  interest  at  4|-%  and  is  due  May  20,  1923. 

As  the  third  and  fourth  loans  were  issued  at  a  rate  of  interest 
higher  than  that  of  the  second,  the  Government  offered  to  ex- 
change 4%  bonds  for  4^%  bonds,  provided  the  change  was  made 
before  November  9,  1918. 

Investment  Value  of  the  Liberty  Loan  Bonds. 
Illustration : 

Suppose  you  bought  a  Fourth  Liberty  Loan  Bond  of    the  SlOO  de- 
nomination. 

Your  annual  income  from  the  bond  at  the  rate  of  4^%  will  be 

4i%  of  $100  =  .0425  XSIOO  =S4.25. 

On  October  15,  1938,  your  bond  will  be  paid,  by  the  United  States 
Government,  and  you  will  be  paid  SlOO  in  gold. 

The  interest  on  the  Libert}^  Loan  Bonds  is  payable  semi-an- 
nually, or  every  six  months.  Interest  on  these  bonds  is  paid  by 
coupons,  which  are  attached  to  the  bond,  and  for  which  any  bank 
will  pay  cash.  The  bonds  are  issued  in  denominations  of  S50, 
$100,  S500,  SIOOO,  SoOOO,  S10,000,  $50,000,  and  $100,000. 


108  LIBERTY  LOAN  BONDS 


WRITTEN  APPLICATIONS 


.1.  Find  the  annual  income  on  $1000  invested  in  First  Liberty 
Loan  Bonds. 

2.  Find  the  annual  income  on  $3500  invested  in  Third  Liberty 
Loan  Bonds. 

3.  A  man  invested  $200  in  each  of  the  first  four  Liberty  Loans. 
What  is  the  annual  income  from  these  investments? 

4.  A  man  has  $3000  invested  in  the  First  Liberty  Loan,  $4000 
in  the  Second,  $5000  in  the  Third,  and  $8000  in  the  Fourth. 
What  is  his  total  annual  income  from  these  four  investments  ? 

5.  The  total  subscription  to  the  First  Liberty  Loan  Bonds 
was  $3,035,226,850.  Find  the  annual  interest  payment  made  by 
the  Government  on  this  loan. 

6.  The  total  number  of  subscribers  to  the  First  Liberty  Loan 
was  4,500,000.  What  was  the  average  amount  subscribed  by  each 
subscriber  ? 

7.  The  total  subscriptions  to  the  Third  and  Fourth  Liberty 
Loans  were  $4,176,516,850,  and  $6,989,047,000,  respectively. 
Find  the  annual  interest  payment  made  by  the  Government  on 
these  two  loans. 


EIGHTH   GRADE 

BANKING 

A  Bank  is  an  institution  for  lending,  issuing,  or  caring  for 
money,  and  for  performing  other  financial  service. 

From  the  standpoint  of  organization  and  control,  banks  may 
be  classed  as  national,  state,  and  private. 

A  National  Bank  is  a  bank  authorized  and  inspected  by  the 
United  States  Government.  It  has  the  right  to  issue  national 
bank  notes  which  are  used  as  money. 

A  State  Bank  is  a  bank  authorized  and  inspected  by  a  State 
Government. 

A  Private  Bank  is  conducted  by  an  individual  or  company 
without  the  inspection  or  control  of  either  the  Federal  or  State 
Governments. 

From  the  nature  of  the  business  which  they  do,  banks  are  classed 
as  Commercial  hanks,  Savings  banks,  or  Trust  companies. 

A  Commercial  Bank,  sometimes  called  a  Bank  of  Deposit,  re- 
ceives money  for  safe-keeping,  makes  loans,  cashes  checks  and 
drafts,  collects  accounts,  issues  letters  of  credit,  and  performs 
other  kinds  of  financial  service. 

A  Savings  Bank  receives  and  invests  savings  and  pays  interest 
on  deposits  at  stated  times. 

A  Trust  Company  is  empowered  by  state  law  to  accept  and 
execute  trusts,  to  receive  deposits  of  money  and  other  personal 
property,  and  to  lend  money  on  real  and  personal  security. 

Federal  Reserve  Banks  are  central  or  regional  banks  under  the 
control  of  the  United  States  Government.  They  are  often  re- 
ferred to  as  "  the  bankers'  banks/'  and  their  character  and  work 
will  be  discussed  after  general  banking  has  been  described. 

109 


no 


BANKING 


THE  PRACTICE  OF  GENERAL  BANKING 

Opening  an  Account  is  the  first  step  in  securing  the  services  of 
a  bank.  The  depositor,  or  customer,  places  money  in  the  bank  to 
be  credited  to  his  account.  If  he  is  not  personally  known  to  some 
official  in  the  bank,  he  must  first  be  "  identified,"  that  is,  he  must 
be  introduced  by  a  reliable  person  known  to  the  bank.  His  signa- 
ture is  recorded  by  the  bank  in  order  to  verify  it  when  signed  to 
checks  or  to  other  documents. 

A  Deposit  Slip,  describing  in  detail  the  items  of  his  deposit,  is 
made  out  by  the  depositor  and  presented  to  the  teller. 

A  Pass  Book  is  given  him,  in  which  are  entered  the  sums  de- 
posited from  time  to  time. 

A  Check  Book  is  also  given  him  to  enable  him  to  order  the  bank 
to  pay  various  sums  from  his  account. 

OPENING   AN   ACCOUNT  WITH   A   BANK 


DEPOSITED  IN 

FORT  DEARBORN  NATIONAL  BANK 

For  Account  of 


Checks  on  Chicago 
P.  0.  and  Express  Orders 


hs 
«/ 


Items  Outside  Chicago 


Currency 
Gold 
Silver 
Total 


#■ 


Zo 


/-T 


jf_Z£^ 


¥0 

3^. 


oo 


oo 


Z£ 


/jT 


At  the  left  is  shown  a  deposit 
slip  filled  out  to  open  an  account 
for  Mr.  Frederick  Anderson  in 
the  Fort  Dearborn  National  Bank, 
Chicago,  Illinois.  The  deposit  slip 
provides  a  space  in  which  the 
depositor  enters  local  checks,  as 
well  as  postal  and  express  money 
orders ;  while  checks  payable  by 
banks  outside  of  Chicago  are  listed 
in  a  separate  group.  The  deposit 
of  $256.15  is  credited  to  Mr.  Ander- 
son on  the  books  of  the  bank,  and 
a  similar  entry  is  made  in  his 
pass  book. 


OPENING  AN  ACCOUNT  111 

WRITTEN   APPLICATIONS 

Make  out  in  your  own  name  deposit  slips  for  each  of  the  fol- 
lowing : 

1.  Currency,  $48.00;  Gold,  $15.00;  Silver,  $18.85.  Checks: 
First  National  of  Minneapolis,  $24.90;  Commonwealth  Trust 
Co.  of  Philadelphia,  $151.65;  First  National  of  Chicago,  $200.00. 

2.  Currency,  $165.00;  Gold,  $35;  Silver,  $18.30.  Checks: 
Foiirth  National  of  Minneapolis,  $49.75;  Franklin  Trust  Co.  of 
New  York,  $54.10;  Farmer's  National  of  Albany,  $162.40;  City 
Bank  of  San  Francisco,  $119.87. 

3.  Currency,  $245.00;  Silver,  $19.70.  Checks:  First  National 
of  Denver,  $136.00;  Mechanics  National  of  Worcester,  $450.00; 
Corn  Exchange  of  New  York,  $178.50;  Fidelity  Trust  Co.  of 
Kansas  City,  $67.00. 

4.  Currency,  $275  ;  Gold,  $20  ;  Silver,  $19.90.  Checks  :  First 
National  of  Detroit,  $287.10;  Commercial  Trust  Co.  of  Philadel- 
phia, $98.15;  Franklin  Realty  Trust  Co.  of  Boston,  $175.90; 
Maiden  Savings  Bank,  $196.12. 

5.  Checks :  Second  National  of  Cleveland,  $276.50 ;  Ritten- 
house  Trust  Co.  of  Philadelphia,  $115  ;  Chemical  National  Bank  of 
New  York,  $1500.     Currency,  $276.     Silver,  $269.40. 

6.  Currency,  $376;  Gold,  $45;  Silver,  $198.70.  Checks: 
Hanover  National  of  New  York,  $1100;  Mechanics  National  of 
Worcester,  $378.50;  Central  Union  Trust  Co.  of  New  York, 
$1156.20 ;  Fort  Dearborn  National  of  Chicago,  $3120.57. 

7.  Currency,  $119;  Gold,  $45;  Silver,  $37.20.  Checks:  First 
National  of  Chicago,  $145.00;  First  National  of  Galesburg, 
$100.00 ;  Third  National  of  Philadelphia,  $154.50 ;  Fletcher  Trust 
Co.  of  Indianapolis,  $95.75;  First  National  of  Boston,  $85.10; 
Second  National  of  Cleveland,  $45.00;  Chemical  National  of 
New  York,  $275.00;  First  National  of  Augusta,  Ga.,  $78.75. 


112  BANKING 


A  Bank  Check.     A  bank  check  is  a  written  order  made  by  a 
depositor  directing  the  bank  to  pay  a  certain  sum  from  his  deposit. 


Fort  Dearborn  JSTational  Bank  2-12 


cTL^^te^e.^rry^'^   ^o  .— > — ^ ^ — T>onays 


The  use  of  checks  simpUfies  the  transacting  of  business,  for  it  permits 
the  payment  of  bills  or  other  obligations  without  the  transfer  of  actual 
cash.  Another  advantage  in  the  use  of  checks  is  that  the  accurate  record 
of  the  banks  who  handle  them  serves  as  a  verification  in  case  of  need. 
Moreover,  the  loss  of  a  check  is  not  usually  a  serious  matter,  for  the 
maker  may  stop  the  payment  of  it,  and,  at  a  later  date,  issue  a  duplicate. 

Forms  of  Indorsement.  Before  a  bank  pays  a  check  it  requires 
upon  the  back  of  the  check  the  signature  of  the  person  to  whom 
payment  is  made.  This  indorsement  is  a  receipt  from  the  payee 
to  the  bank  making  the  payment. 

When  a  check  is  made  payable  to  an  individual  '^  or  order  '' 
it  is  negotiable;  that  is,  it  may  be  collected  by  any  one  known  to 
the  bank  to  which  it  is  presented.  When  a  person  or  firm  mails 
a  check  for  deposit,  it  is  customary  to  indorse  it  with  the  phrase 
"  For  Deposit  Only,"  or,  '^  For  Deposit  to  the  credit  of  "  followed 
by  the  name  of  the  payee.  No  bank  would  pay  a  check  indorsed 
in  this  way  if,  through  loss  or  otherwise,  it  fell  into  the  wrong  hands 

WRITTEN   APPLICATIONS 

1.  Write  a  check  for  one  hundred  dollars,  dated  to-day,  payable 
to  Henry  W.  Breed,  drawn  on  the  Union  Bank  of  Indianapolis, 
and  signed  by  yourself. 


THE  BANK  CHECK  113 

2.  Write  a  check  for  forty-seven  dollars  and  fifty-eight  cents, 
dated  to-day,  payable  to  Charles  H.  Bronson,  and  drawn  on  the 
Commonwealth  Trust  Company  of  Philadelphia,  and  signed  by 
Thomas  B.  Wilcox. 

3.  Write  a  check  for  two  hundred  fifty  dollars,  dated  January 
10,  1919,  payable  to  Thomas  D.  Raymond,  and  drawn  on  the 
Mechanics  National  Bank  of  Birmingham,  Ala.,  and  signed  by 
Charles  H.  Swift. 

4.  Write  a  check  for  one  hundred  seventy-eight  dollars  and 
eleven  cents,  dated  October  12,  1918,  payable  to  George  Carr, 
and  drawn  on  the  First  National  Bank  of  Louisville,  Ky.,  by 
William  White. 

5.  Write  a  check  for  fourteen  dollars,  dated  to-day,  payable  to 
yourself,  and  drawn  on  the  West  End  Trust  Company  of  Phila- 
delphia, Pa.,  by  Thomas  Stocking.  Indorse  this  check  yourself, 
and  show  the  subsequent  indorsement  of  the  Cook  Hardware 
Company,  to  whom  you  gave  it  in  payment  of  a  bill. 

6.  W>ite  a  check  for  seventy-five  dollars,  dated  July  11,  1919, 
payable  to  yourself,  and  drawn  on  the  Corn  Exchange  Bank  of 
New  York  City  by  J.  M.  Green.  Show  how  you  would  indorse 
this  check  in  mailing  it  to  your  bank  for  deposit. 

Keeping  a  Record  of  a  Bank  Account.  The  depositor  should 
keep  a  careful  record  of  his  deposits  and  withdrawals.  Such  a 
record  is  kept  on  the  check  stubs,  and  without  it  he  is  liable  to 
draw  checks  for  more  money  than  he  has  to  his  credit. 

WRITTEN    APPLICATIONS 

1.  A  merchant's  bank  balance  on  June  30  is  $1275.90.  During 
July  he  deposits  $1871.95,  and  checks  out  $2705.10.  What  is 
his  balance  on  Juty  31? 

2.  A  merchant's  bank  balance  on  August  1  was  $549.20,  and 
during  the  month  he  deposited  $2735.60  and  checked  out  $1988.54. 
What  was  his  balance  on  August  31? 


114  BANKING 

3.  On  the  first  day  of  the  month  a  business  firm  has  a  balance 
on  hand  of  $2140.15,  and  in  that  month  their  deposits  are  $480.19, 
$317.42,  $694.48,  $510.00,  $178.10,  $1039.54,  $687.07,  and  $2119.56. 
In  the  same  month  the  firm  drew  checks  amounting  to  $4566.18. 
Find  the  balance  on  deposit  to  the  firm's  credit  at  the  end  of  the 
month. 

4.  During  the  week  of  April  2,  1918,  a  manufacturer  made  de- 
posits of  $2715.10,  $3510.19,  $1750,  $1862.57,  $697.25,  and  $598.69, 
on  the  six  business  days  respectively.  He  withdrew  $125  on  each 
of  the  first  five  days  of  the  week,  and  $2490.50  on  Saturday. 
Find  the  difference  between  the  total  of  the  deposits  and  the  total 
of  the  withdrawals  for  that  week. 

5.  On  Monday  morning  at  the  beginning  of  business  a  merchant 
had  a  balance  of  $2917.12  in  the  bank.  On  that  day  he  deposited 
$890  and  checked  out  $1137.12.  On  Tuesday  he  deposited  $762.40 
and  checked  out  $196.37  ;  on  Wednesday  he  deposited  $1317  and 
checked  out  $2762.10;  and  on  Thursday  he  deposited  $1678.47 
and  checked  out  $584. 14.  Find  the  amount  of  his  balance  at  the 
end  of  each  of  the  four  business  days. 

6.  At  the  beginning  of  a  week  the  balance  on  deposit  in  an  account 
was  $241.50,  and  deposits  of  $294.50,  $161.20,  $351.80,  $96.42, 
$171.11,  and  $840  were  made  on  six  consecutive  days.  The  daily 
withdrawals  for  the  same  six  days  were  respectively  $164.10, 
$35.90,  $246.91,  $101.87,  $211.19,  and  $67.85.  What  was  the 
balance  remaining  at  the  end  of  the  week? 

7.  At  the  opening  of  business  on  a  certain  Monday  morning  a 
merchant's  balance  in  the  bank  was  $1974.38.  On  that  day  he 
deposited  $690.11  and  checked  out  $482.10.  On  Tuesday  he 
deposited  $542.13  and  checked  out  $376.14;  on  Wednesday  he 
deposited  $493.81 ;  on  Thursday  he  checked  out  $750 ;  on 
Friday  he  deposited  $1109.18  and  checked  out  $1500;  and  on 
Saturday  he  deposited  $2118  and  checked  out  $2545.50.  What 
was  the  amount  of  his  balance  at  the  close  of  business  on  Saturday? 


BANK  DISCOUNT  115 

BANK   DISCOUNT 

Borrowing  Money  from  a  Bank.  In  carrying  on  their  busi- 
ness, most  business  men  have  need  at  times  of  more  money  than 
they  have  on  hand.  In  such  cases  the  banks  loan  them  money  on 
promissory  notes,  which  vary  in  form. 

Bank  Discount  is  the  simple  interest  on  the  money  loaned, 
collected  in  advance  for  the  time  for  which  the  loan  is  made. 

The  Term  of  Discount  is  the  number  of  days  from  the  day  on 
which  the  note  is  discounted  to  the  day  on  which  the  note  is  due. 

The  Face  of  a  Note  is  the  sum  written  in  the  note. 

The  Proceeds  of  a  Note  are  the  balance  remaining  after  deduct- 
ing the  discount  from  the  face  of  the  note. 

Illustration : 

If  $2500  is  borrowed  from  a  bank  for  60  days  at  6%,  the  bank  cal- 
culates the  interest  on  S2500  for  60  days,  or  $25. 

This  interest,  or  discount,  is  deducted  from  the  face  of  the  note.     And, 
$2500 -$25,  or  $2475,  is  paid  over  to  the  borrower. 
In  this  case : 

The  Face  of  the  Note  =$2500. 
The  Term  of  Discount  =  60  days. 
The  Rate  of  Discount  =6%. 
The  Bank  Discount     =$25. 
The  Proceeds  =$2475. 

At  the  end  of  the  60  days,  when  the  note  is  due,  the  borrower  pays  the 
bank  $2500. 

WRITTEN   APPLICATIONS 

Find  the  discount  and  the  proceeds  when  the  face,  the  term  of 
discount,  and  the  rate,  respectively,  are : 

1.  $300,  30  days,  6%.  6.  $1000,  30  days,  6%. 

2.  $350,  60  days,  6%.  7.  $1500,  60  days,  5%. 

3.  $450,  60  days,  6%.  8.  $2250,  90  days,  6%. 

4.  $575,  90  days,  5%.  9.  $2500,  90  days,  5%. 

5.  S750,  60  days,  6%.  10.  $3000,  60  days,  6%. 


116  BANKING 

WRITTEN   APPLICATIONS 

1.  Make  out  a  60-day  note  for  $100,  dated  to-day,  and  paj^able 
by  yourself  at  your  local  bank. 

2.  Make  out  a  60-day  note  for  $350,  dated  to-day,  and  payable 
by  John  Fox  at  the  First  National  Bank  of  Montgomery,  Alabama. 

3.  Make  out  a  30-day  note  for  $500,  signed  by  Harrison  Field, 
payable  at  the  First  National  Bank  of  Chicago,  and  dated  August 
4,  1919. 

4.  Make  out  a  note  for  $500,  dated  to-day,  and  signed  by  your- 
self. If  this  money  is  borrowed  from  your  local  bank,  find  the 
proceeds  if  the  note  runs  60  days. 

5.  Make  out  a  note  in  which  French  &  Monroe,  merchants, 
borrow  $2500  from  the  Fort  Dearborn  National  Bank  of  Chicago 
for  60  days,  and  find  the  proceeds  of  this  note  if  the  interest  rate 
is  5%. 

6.  Adams,  Jackson  &  Co.  borrow  $3000  from  the  Corn  Exchange 
Bank  of  New  York  on  June  1,  1919.  If  the  note  runs  60  days, 
and  if  the  rate  of  discount  is  5%,  find  the  proceeds  of  the  note. 
Make  a  note  to  show  the  transaction. 

7.  Flint  and  Harrison  borrow  $4500  from  the  First  National 
Bank  of  Chicago,  and  their  note  is  dated  March  10,  1919.  The 
note  is  to  run  60  days,  and  the  bank  discounts  it  on  the  date  it  is 
made,  at  5^%.  Find  the  proceeds  of  the  note.  Make  a  note  to 
show  the  transaction. 

If  a  note  falls  due  on  a  Sunday  or  on  a  legal  holiday  its  payment  is 
due,  in  most  states,  on  the  next  succeeding  business  day,  and  the  term  of 
discount  includes  that  day.  A  bank  usually  demands  that  a  note  which 
it  has  discounted  shall  be  payable  at  that  bank. 

Discounting  Interest-bearing  Notes.  A  business  man  fre- 
quently holds  the  note  of  another  business  man  or  firm,  and  needs 
to  use  the  money  before  the  note  legally  becomes  due.  While  he 
cannot  compel  the  payment  of  the  note  before  the  end  of  the  time 
named  in  it,  he  can  obtain  the  cash  by  discounting  it  at  his  bank. 


BANK  DISCOUNT  117 

Illustration : 

A  merchant  holds  a  note  for  1500  dated  April  10.  The  note  is 
to  run  4  months  and  bears  interest  at  5%,  but  on  May  29  the  mer- 
chant finds  immediate  need  for  the  money  and  discounts  the  note 
at  his  bank.  The  bank  actually  purchases  the  note,  and  deter- 
mines the  amount  to  be  paid  to  the  merchant  by  the  following 
process. 

The  note  is  due  4  months  after  April  10,  or  on  Au^st  10. 

The  bank  takes  it  on  May  29,  hence,  they  must  hold  it  from  May  29 
to  August  10,  or  73  days. 

The  interest  on  the  note  from  April  10  to  August  10  is  $8.33. 

Therefore,  the  note  is  worth  on  August  10,  $508.33. 

The  bank  must  wait  73  days  for  this  amount,  or  must  advance  this 
amount  less  the  interest  upon  it  for  that  time  at  6%. 

The  discount,  therefore,  is  the  interest  on  $508.33  for  73  days  at  6%. 

This  discount  is  $6.10.     (By  Method  of  Exact  Interest,  p.  100.) 

Therefore,  the  holder  of  the  note  receives  for  it  $508.33 —$6.10,  or 
$502.23,  the  proceeds. 

The  actual  value  of  the  note  at  maturity  is  its  face  value  plus  the 
interest  at  the  rate  named  in  the  note  for  the  full  time  of  the  note. 

The  actual  amount  received  by  the  holder  when  he  discounts  it,  or 
the  proceeds,  is  the  value  of  the  note  at  maturity  less  the  interest  on  that 
amount  from  the  day  he  discounts  it  to  the  day  it  is  due,  at  the  bank's 
rate  of  discount. 

WRITTEN   APPLICATIONS 

In  each  of  the  following  find  (1)  the  date  of  maturity,  (2)  the 
term  of  discount,  (3)  the  bank  discount,  and  (4)  the  proceeds : 

1.  A  60-day  note  for  $1000  without  interest  and  dated  March  1 
is  discounted  on  the  same  day  at  6%. 

2.  A  60-day  note  for  $1100  without  interest  and  dated  April  20 
is  discounted  on  the  same  day  at  5%. 

3.  A  90-day  note  for  $100  bearing  interest  at  6%  and  dated 
March  10  is  discounted  April  9  at  5%. 

4.  A  60-day  note  for  $1000  bearing  interest  at  5%  is  dated 
January  1  and  is  discounted  on  that  day  at  the  same  rate. 


118  BANKING 

5.  A  30-day  note  for  $1200  bearing  interest  at  5%  is  dated 
March  10,  and  is  discounted  on  March  16  at  the  same  rate. 

6.  A  90-day  note  for  $1500  bearing  interest  at  5%  is  dis- 
counted 30  days  after  date  at  6%. 

7.  A  90-day  note  for  $2000  bearing  interest  at  6%  is  discounted 
30  days  after  date  at  5%. 

8.  A  note  dated  June  1  is  to  run  60  days.     The  face  is  $1200, 
and  the  interest  rate  5%.     The  note  is  discounted  June  15  at  5%. 

9.  Find  the  proceeds  of  the  following  note. 

S250.  Springfield,  Illinois,  Jan.  10,  1919. 

Sixty  days  after  date,  for  value  received,  I  promise  to  pay 
George  M.  Stacey,  or  order,  two  hundred  fifty  dollars,  with  interest 
at  6%,  at  the  First  National  Bank. 

Discounted,  Jan.  25,  at  5%.    *  F.  W.  Wilson. 

10.   Find  the  proceeds  of  the  following  note. 

$450.  Richmond,  Virginia,  August  1,  1919. 

Ninety  days  after  date,  for  value  received,  I  promise  to  pay 
Brown,  Nash  &  Company,  or  order,  four  hundred  fifty  dollars, 
with  interest  at  5%,  at  the  Fourth  Street  National  Bank. 

Discounted,  September  20,  at  6%.  R.  M.  Lansing. 

Finding  the  Face  of  a  Note  when  the  time,  the  rate,  and  the 
proceeds  are  given. 

Illustration : 

James  Mills  wishes  to  borrow  money  for  60  days  to  pay  a  debt 
of  $1980.     At  6%  interest,  what  will  be  the  face  of  his  note? 

The  interest  on  $1.00  for  60  days  at  6%  =$.01. 
Hence,  the  proceeds  of  $1.00  for  60  days  at  6%  will  be 

$1.00 -$.01  =$.99. 
Dividing  the  given  proceeds,  $1980,  by  the  proceeds  of  $1  for  the 
given  time  and  at  the  given  rate,  we  have 

$1980  ^$.99  =  $2000. 
That  is,  he  must  borrow  $2000  in  order  that  the  proceeds  immediately 
available  shall  be  $1980. 


BANK  DISCOUNT  '  119 

WRITTEN   APPLICATIONS 

1.  The  proceeds  of  a  note  for  90  days  at  6%  were  $295.50. 
What  was  the  face  of  the  note  ? 

2.  The  proceeds  of  a  note  for  60  days  at  5%  were  $1487.50. 
What  was  the  face  of  the  note? 

3.  The  proceeds  of  a  note  for  60  days  at  6%  were  $495.  What 
was  the  face  of  the  note  ? 

4.  The  proceeds  of  a  note  for  90  days  at  6%  were  $641.87. 
What  was  the  face  of  the  note  ? 

5.  A  merchant  wishes  to  borrow  $2000  for  3  months  at  6%. 
For  what  amount  shall  he  give  his  note  ? 

6.  A  merchant  wishes  to  raise  $2000  by  having  his  60-day  note 
discounted  at  his  bank  at  5%.  For  what  amount  shall  he  give 
his  note? 

7.  For  what  amount  must  a  4-months  note  bearing  interest  at 
6%  be  written  if  the  maker  wishes  to  raise  exactly  $1200  by  dis- 
counting it  on  the  day  it  is  written? 

8.  For  what  amount  must  a  real  estate  dealer  make  a  90-day 
note  so  that  a  trust  company  will  discount  it  at  4|-%  and  turn 
over  $20,000  to  him? 

9.  In  paying  for  a  new  house  a  man  needed  $3500.  If  he  bor- 
rowed this  sum  from  his  bank,  and  on  a  note  made  to  run  90  days 
and  bearing  6%  interest,  for  what  sum  did  he  write  his  note  so  as 
to  obtain  just  the  sum  he  needed? 

10.  Write  a  note  dated  at  Grand  Rapids,  Michigan,  May  1, 1919, 
made  by  Robert  Corson  for  $150,  and  payable  at  the  First  National 
Bank  of  Grand  Rapids,  with  6%  interest ;  the  note  to  be  payable 
to  the  order  of  Everett  Kellogg,  and  to  run  90  days. 

11.  Write  a  note  dated  at  Topeka,  Kansas,  November  15, 1919, 
payable  after  60  days  to  the  Monroe-Franklin  Company,  at  the 
First  National  Bank  of  Topeka,  with  6%  interest,  and  signed  by 
Fels  &  Babbitt  for  $1200.  Discount  this  note  on  November  27  at 
4%,  and  find  the  proceeds. 


120  BANKING 


COMPOUND   INTEREST 


Compound  Interest  is  interest  on  both  the  principal  and  the 
unpaid  interest,  the  principal  and  interest  being  combined  at 
regular  intervals. 

Illustration : 

$100  at  6%  interest  for  1  year  brings  interest  =$6. 

$100 +$6  =  $106,  the  amount  drawing  interest  at  beginning  of  2d  year. 

$106  at  6%  interest  for  1  year  brings  interest  =$6.36. 

$106 +$6.36  =  $112.36,  the  amount  drawing  interest  at  beginning  of 
3d  year. 

$112.36  at  6%  interest  for  1  j^ear  brings  interest  =.$6.74. 

.$112. 36+$6.74  =  $119.10,  the  amount  drawing  interest  at  beginning  of 
4th  year. 

In  the  illustration  the  interest  is  calculated  and  added  annually. 

Interest  may  be  added,  or  compounded,  annually,  semi-annually, 
quarterly,  or  at  any  other  intervals  agreed  on  in  a  contract. 

Most  of  the  savings  banks  allow  compound  interest  when  sums 
deposited  bear  interest  for  a  full  period. 

Application  of  Compound  Interest 

I.  To  calculate  the  compound  interest  on  a  given  principal, 
for  a  given  time,  at  a  given  rate. 

Illustration :  "^ 

Find  the  compound  interest  on  $300  for  3  yr.  6  mo.  at  6%. 

Principal $300.00 

Interest  for  1  yr.  at  6% 18.00 

Principal  at  beginning  of  2d  yr 318.00 

Interest  for  2d  yr.  at  6% 19.08 

Principal  at  beginning  of  3d  yr 337.08 

Interest  for  3d  yr.  at  6% 20.22 

Principal  at  beginning  of  4th  yr 357.30 

Interest  for  6  mo 10.72 

Amount  of  .$300  for  3  yr.  6  mo.  at  6%    ....  368.02 

Then  :     $368.02  -$300.00  =  $68.02,  the  compound  interest.     Result. 


COMPOUND  INTEREST  121 

WRITTEN    APPLICATIONS 

Find,  when  compounded  annually,  the  interest  on 

1.  $400  for  3  yr.  at  6%.  4.    $1000  for  5  yr.  at  6% 

2.  $500  for  3  yr.  at  5%.  5.    $1500  for  4  yr.  at  6%. 

3.  $600  for  4  yr.  at  4%.  6.    $300  for  2  yr.  6  mo.  at  6%. 

7.  $400  for  3  yr.  4  mo   at  5%. 

8.  $450  for  3  yr.  6  mo.  10  da.  at  6%. 

9.  $525.50  for  2  yr.  5  mo.  20  da.  at  6%. 

10.  $754.50  for  3  yr.  2  mo.  15  da.  at  6%. 

11.  Find  the  interest,  compounded  semi-annually,  on  $1200  for 
2  yr.  6  mo.  at  3%. 

12.  Find  the  amount  of  $450  for  2  yr.  3  mo.,  compounded 
annuall}^  at  1^%. 

II.  To  find  the  compound  interest  on  a  given  principal,  for  a 
given  time,  and  at  a  given  rate,  by  use  of  the  Interest  Table. 

The  Compound  Interest  Table  is  constantly  used  by  savings 
banks,  bond  brokers,  and  insurance  companies.  The  table  gives 
the  amount  of  $1  for  periods  from  1  to  20  years,  and  at  different 
rates.     The  use  of  the  table  is  readily  understood  from  the 

Illustration : 

Find  the  compound  interest  on  $500  for  6  years  at  4%. 

In  the  column  headed  "4%"  and  opposite  "6"  in  the  column  of 
"years"  we  find  1.265319. 

This  number  is  the  amount  of  $1  for  the  given  time  at  the  given  rate. 

Therefore,  the  amount  of  $500  =500  X$  1.2653 19  =  $632.6595. 

And:  $632.66 -$500.00  =  $132.66,  the  compound  interest  required. 
Result. 


122 


BANKING 


COMPOUND  INTEREST   TABLE 

Amount  of  $1,  at  various  rates,  compound  interest,  1  to  20  years 


Years 

1% 

U% 

lJ-% 

2% 

2i% 

3% 

1 

1.010000 

1.012500 

1.015000 

1.020000 

1.025000 

1.030000 

2 

1.020100 

1.025156 

1.030225 

1.040400 

1.050625 

1.060900 

3 

1.030301 

1.037971 

1.045678 

1.061208 

1.076891 

1.092727 

4 

1.040604 

1.050945 

1.061364 

1.082432 

1.103813 

1.125509 

5 

1.051010 

1.064082 

1.077284 

1.104081 

1.131408 

1.159274 

6 

1.061520 

1.077383 

1.093443 

1.126162 

1.159693 

1.194052 

7 

1.072135 

1.090850 

1.109845 

1.148686 

1.188686 

1.229874 

8 

1.082857 

1.104486 

1.126493 

1.171659 

1.218403 

1.266770 

9 

1.093685 

1.118292 

1.143390 

1.195093 

1.248863 

1.304773 

10 

1.104622 

1.132271 

1.160541 

1.218994 

1.280085 

1.343916 

11 

1.115668 

1.146424 

1.177949 

1.243374 

1.312087 

1.384234 

12 

1.126825 

1.160755 

1.195618 

1.268242 

1.344889 

1.425761 

13 

1.138093 

1.175264 

1.213552 

1.293607 

1.378511 

1.468534 

14 

1.149474 

1.189955 

1.231756 

1.319479 

1.412974 

1.512590 

15 

1.160969 

1.204829 

1.250232 

1.345868 

1.448298 

1.557967 

16 

1.172579 

1.219889 

1.268986 

1.372786 

1.484506 

1.604706 

17 

1.184304 

1.235138 

1.288020 

1.400241 

1.521618 

1.652848 

18 

1.196148 

1.250477 

1.307341 

1.428246 

1.559659 

1.702433 

19 

1.208109 

1.266108 

1.326951 

1.456811 

1.598650 

1.753506 

20 

1.220190 

1.281935 

1.346855 

1.485947 

1.638616 

1.806111 

Years 

3^% 

4% 

4J% 

5% 

6% 

7% 

1 

1.035000 

1.040000 

1.045000 

1.050000 

1.060000 

1.070000 

2 

1.071225 

1.081600 

1.092025 

1.102500 

1.123600 

1.144900 

3 

1.108718 

1.124864 

1.141166 

1.157625 

1.191016 

1.225043 

4 

1.147523 

1.169859 

1.192519 

1.215506 

1.262477 

1.310796 

5 

1.187686 

1.216653 

1.246182 

1.276282 

1.338226 

1.402552 

6 

1.229255 

1.265319 

1.302260 

1.340096 

1.418519 

1.500730 

7 

1.272279 

1.315932 

1.360862 

1.407100 

1.503630 

1.605782 

8 

1.316809 

1.368569 

1.422101 

1.477455 

1.593848 

1.718186 

9 

1.362897 

1.423312 

1.486095 

1.551328 

1.689479 

1.838459 

10 

1.410599 

1.480244 

1.552969 

1.628895 

1.790848 

1.967151 

11 

1.459970 

1.539454 

1.622853 

1.710339 

1.898299 

2.104852 

12 

1.511069 

1.601032 

1.695881 

1.795856 

2.012197 

2.252192 

13 

1.563956 

1.665074 

1.772196 

1.885649 

2.132928 

2.409845 

14 

1.618695 

1.731676 

1.851945 

1.979932 

2.260904 

2.578534 

15 

1.675349 

1.800944 

1.935282 

2.078928 

2.396558 

2.759032 

16 

1.733986 

1.872981 

2.022370 

2.182875 

2.540352 

2.952164 

17 

1.794676 

1.947901 

2.113377 

2.292018 

2.692773 

3.158815 

18 

1.857489 

2.025817 

2.208479 

2.406619 

2.854339 

3.379932 

19 

1.922501 

2.106849 

2.307860 

2.526950 

3.025600 

3.616528 

20 

1.989789 

2.191123 

2.411714 

2.653298 

3.207136 

3.869684 

COMPOUND  INTEREST 


123 


ORAL   PRACTICE 

Find  in  the  table  and  read  the  amount  of  $1  for 


1.  3  years  at  2%. 

2.  4  years  at  3%. 

3.  4  years  at  4%. 


10. 
11. 
12. 
13. 
14. 
15. 
16. 
17. 
18. 


10  years  at  6%. 

10  years  at  11%. 

11  years  at  2^%. 

12  years  at  4%. 

15  years  at  5%. 

16  years  at  3%. 

17  years  at  4^%. 

19  years  at  7%. 

20  years  at  5%. 


4.  5  years  at  5%. 

5.  6  years  at  6%. 

6.  7  years  at  4%. 

7.  8  years  at  4%. 

8.  10  years  at  5%. 

9.  10  years  at  3^%. 

In  compound  interest  the  practice  is  to  compound  annually 
unless  otherwise  specified.  If  compounded  semi-annually,  or 
twice  each  year,  the  rate  at  each  compounding  is  one  half  of  the 
given  rate ;  if  quarterly,  the  rate  is  one  fourth  the  given  rate. 

Illustration : 

Find  the  amount  of  $1000  for  5  years  at  compound  interest, 
compounded  semi-annually  at  5%. 

Since  the  interest  is  compounded  semi-annually,  there  are  10  periods. 
The  rate  for  each  is  one  half  the  given  rate,  or  2i%, 
Therefore,  find  the  amount  of  $2000  for  10  years  at  2i%. 
Using  the  table : 

Amount  of  $1  for  10  years  at  2^%  =$1.280085  (10th  Hne,  5th  column). 
Hence,  the  amount  of  $1000  for  the  same  time  at  the  same  rate  is 
1000  X$1.280085  =  $1280.085.     $1280.09.     Result. 

WRITTEN   APPLICATIONS 

Using  the  table,  find  the  compound  interest  on 

1.  $1200  for  3  yr.  6  mo.  at  6%. 

2.  $1200  for  4  yr.  4  mo.  at  6%. 

3.  $1500  for  5  yr.  6  mo.  at  5%. 

4.  $1500  for  4  yr.  9  mo.  at  4^%. 

5.  $1500  for  6  yr.  6  mo.  at  4%. 


124 


BANKING 


6.  $1875  for  4  yr.  9  mo.  at  S^%. 

7.  $2000  for  5  yr.  4  mo.  at  4^%. 

8.  $2100  for  6  yr.  3  mo.  at  3^%. 

9.  $2400  for  4  yr.  10  mo.  at  5%. 

10.  $256.50  for  4  yr.  6  mo.  15  da. 

11.  $350.25  for  5  yr.  8  mo.  10  da. 

12.  $450.80  for  6  yr.  6  mo.  at  5%,  compounded  semi-annually. 

13.  $565.11  for  4  yr.  8  mo.  at  4%,  compounded  semi-annually. 


at  4%. 

at  4%. 


SAVINGS   BANKS 

Savings  Banks   receive   deposits   in   small   amounts   and   pay 
compound  interest  to  the  depositors. 


DATE 

DEPOSITS 

WITHDRAWALS 

INTEREST 

BALANCE 

i> 

00 

CO 

^ 

0 

0 

00 

& 

0 

0 

00 

"'frioL'] 

/ 

5 

0 

00 

4 

5 

0 

00 

9rLcui^^ 

/ 

00 

00 

5 

5 

0 

00 

Suui 

9 

oo 

5 

5 

9 

oo 

(Zu^h 

3 

0 

0 

oo 

1 

5 

9 

00 

5 

// 

Z 

6 

4 

// 

/ 

Interest  is  credited  by  savings  banks  at  regular  intervals,  usually  on 
January  1  and  July  1  of  each  year.  It  is  common  practice  to  credit 
interest  only  at  the  end  of  each  six  months'  period,  and  to  calculate  the 
interest  for  a  period  upon  the  average  balance  on  deposit  during  that 
period.  However,  there  are  no  fixed  rules  governing  the  practice  of  all 
savings  banks. 


SAVINGS  BANKS  125 

A  common  form  of  bank  book  issued  by  savings  banks  is  illus- 
trated. The  illustration  shows  deposits,  withdrawals,  balances 
resulting  at  each  transaction  or  entry,  interest  credits,  and  the 
final  condition  of  an  account. 

In  the  illustration  the  interest  rate  is  4%,  computed  semi-annually, 
that  is,  2%  interest  is  credited  on  July  1  and  January  1. 

As  an  illustration  of  a  custom  that  is  followed  in  many  places,  the 
interest  for  each  six  months  is  calculated  on  the  smallest  total  balance  to 
the  credit  of  the  depositor  at  any  time  during  the  interest  period.  Thus, 
the  interest  credited  July  1  is  the  interest  for  six  months  at  2%  on  $450, 
the  smallest  balance  on  hand  at  any  one  time  in  that  six  months. 

WRITTEN   APPLICATIONS 

From  each  of  the  following  arrange  a  page  of  a  savings  bank 
book,  and  find  the  balance  due  the  depositor  on  the  date  indicated. 

1.  Deposits:  March  1,  1918,  $200;  July  1,  1918,  $350;  Oc- 
tober 15,  1918,  $150.  Withdrawals:  June  15,  1918,  $50;  August 
30,  1918,  $75;  December  1,  1918,  $50.  Interest  computed  semi- 
annually January  1  and  July  1,  at  4%.  Find  the  balance  due  the 
depositor  on  January  1,  1919. 

2.  Deposits:  January  1,  1918,  $200;  March  1,  1918,  $150;  April 
10,  1918,  $200;  July  10,  1918,  $100;  August  15,  1918,  $190; 
December  10,  1918,  $130.  Withdrawals:  March  10,  1918,  $25; 
April  15,  1918,  $75 ;  September  9,  1918,  $50.  Find  the  depositor's 
balance  on  January  1,  1919,  the  interest  being  compounded  Janu- 
ary 1  and  July  1,  at  3^%. 

3.  Deposits:  October  5,  1917,  $200;  January  1,  1918,  $74; 
March  10,  1918,  $100;  May  5,  1918,  $125;  October  1,  1918,  $275; 
April  7,  1919,  $350;  June  10,  1919,  $100.  Withdrawals:  Febru- 
aiy  10,  1918,  $100;  June  6,  1918,  $100;  December  10,  1918,  $125; 
March  1,  1919,  $150.  Find  the  depositor's  balance  on  July  1, 
1919,  interest  being  compounded  on  January  1  and  July  1,  at  4%. 


126  BANKING 

FEDERAL   RESERVE   BANKS 

The  Federal  Reserve  Act  was  passed  by  the  Congress  of  the 
United  States  in  1916. 

I.  Federal  Reserve  Banks. 

The  entire  United  States  was  divided  by  the  act  into  twelve 
Federal  Reserve  Districts,  each  of  which  includes  a  city  in  which 
is  located  a  Federal  Reserve  Bank.  Every  national  bank  in  a 
district  was  required  to  subscribe  for  an  amount  of  stock  in  the 
Federal  Reserve  Bank  in  that  district  equal  to  six  per  cent  of  its 
own  paid-up  capital  and  surplus. 

The  Paid-up  Capital  of  a  bank  is  the  money  which  has  been  paid  at 
par  for  the  stock  which  has  been  issued.  The  expression,  "at  par,  "  means 
the  face  value  of  the  stock.  Thus,  if  the  capital  of  a  bank  is  divided  into 
shares  of  $100  each,  the  par  value  of  the  shares  is  said  to  be  $100.  The 
Surplus  of  a.  bank  is  accumulated  through  two  sources:  (1)  from  the 
profits  gained  from  its  general  banking  business,  and  (2)  from  the  additional 
amounts  by  which  the  sale  of  capital  stock  exceeds  the  par  value  of  the 
stock  sold.  Thus,  if  a  bank  earned  a  certain  sum  in  a  year,  and  if  it  also 
sold  shares  of  its  stock  at  an  increase  of  $25,000  over  its  par  value,  both 
sums  could  be  added  to  the  surplus  upon  the  vote  of  the  directors. 

The  act  establishing  Federal  Reserve  Banks  stipulates  that  the 
capital  of  each  of  these  banks  must  not  be  less  than  $4,000,000. 

By  the  act  all  of  the  National  Banks  in  a  Federal  Reserve 
District  may  become  members  of  the  Federal  Reserve  Bank  of 
that  district,  and  any  State  Bank  or  any  Trust  Company  which 
complies  with  certain  specified  requirements  may  become  members. 

II.  Federal  Reserve  Notes. 

Upon  depositing  any  United  States  bonds  with  the  Treasurer 
of  the  United  States,  as  stipulated  by  the  laws  relating  to  National 
Banks,  the  Federal  Reserve  BauK  receives  from  the  Comptroller 
of  the  Currency  circulating  notes,  or  currency,  equal  in  value  to 
the  value  of  the  bonds  deposited.  As  this  currency  is  issued  by 
the  twelve  Reserve  Banks  it  will  gradually  replace  certain  exist- 
ing forms,  which  is  one  of  the  objects  of  the  plan. 


FEDERAL  RESERVE  BANKS  '      127 

III.   What  the  Federal  Reserve  Banks  Accomplish. 

The  Federal  Reserve  Banks  have  the  power  to  rediscount  the 
commercial  paper  of  then*  member  banks. 

You  "wdll  recall  that  a  business  man  may  discount  a  note,  or  receive 
cash  in  advance  payment  without  waiting  until  the  note  is  legally  due. 
In  the  same  way  a  Federal  Reserve  Bank  may  discount  this  same  note 
a  second  time,  and  thus  provide  a  larger  supply  of  cash  to  the  member 
bank  presenting  the  note.  Thus  the  Federal  Reserve  Bank  acts  as  "the 
banker's  bank." 

The  constant  redistribution  of  cash  from  certain  points  where 
there  is  an  excess  of  cash  to  other  points  where  the  supply  is  short 
is  one  of  the  principal  powers  of  the  new  bank.  As  a  result,  bankers 
are  spared  those  periods  of  '^  tight  money,"  so  frequent  in  the 
past,  particularly  at  the  close  of  the  year  Vv'hen  the  demands  for 
moving  large  crops  and  for  dividend  payments  are  unusually  heavy. 

The  Twelve  Federal  Reserve  Cities  are 


Boston 

Richmond 

Minneapolis 

New  York 

Atlanta 

Kansas  City 

Philadelphia 

Chicago 

Dallas 

Cleveland 

St.  Louis 

San  Francisco 

The  Reserve  Districts  correspond  in  number  to  the  order  of  the  cities 
given  above.  Thus,  Boston  is  in  District  No.  1,  New  York  in  District 
No.  2,  etc. 

WRITTEN   APPLICATIONS 

1.  How  much  minimum  capital  was  required  by  the  Federal 
Reserve  Act  to  establish  all  of  the  twelve  Federal  Reserve  Banks  ? 

2.  How  many  shares  of  stock  of  each  Federal  Reserve  Bank, 
at  par  value  of  SlOO,  must  have  been  subscribed  before  each  bank 
could  begin  business  ? 

3.  The  paid-up  capital  and  the  surplus  of  a  Chicago  bank 
amount  to  $22,000,000.  When  this  bank  became  a  member  of 
the  Federal  Reserv^e  Bank  in  its  district,  how  much  Federal 
Reserve  Bank  stock  did  this  Chicago  bank  take? 


128       -  BANKING 

4.  The  paid-up  capital  of  a  leading  bank  in  New  York  City  is 
$25,000,000,  and  its  surplus  is  $51,400,000.  How  much  Federal 
Reserve  Bank  stock  was  this  bank  required  to  take  when  it  be- 
came a  member  of  the  Federal  Reserve  Banlc? 

5.  The  maximum  amount  of  stock  which  an  individual  or  a 
company  may  own  in  the  Federal  Reserve  Bank  is  $25,000.  If 
five  state  banks  and  three  insurance  companies  are  permitted  to 
purchase  the  maximum  amount,  what  amount  of  stock  may  they 
together  own? 

6.  In  1918  the  Federal  Reserve  Banks  in  New  York,  Chicago, 
Philadelphia,  and  Boston  earned,  respectively,  $3,718,955.00, 
$1,509,871.00,  $753,874.00,  and  $912,294.00.  Find  the  total  earn- 
ings of  the  four  banks,  and  the  average  rate  of  their  dividends  if 
they  paid  a  total  of  $4,021,677  to  their  stockholders. 

EXCHANGE 

Exchange  is  the  process  by  which  bills  or  debts  may  be  paid 
or  collected  in  distant  places  without  the  actual  transfer  of  cash. 

Domestic  Exchange  is  the  exchange  between  places  in  the  same 
country. 

Foreign  Exchange  is  exchange  between  two  places  in  different 
countries. 

Domestic  Exchange 

The  most  common  forms  of  domestic  exchange  are : 

1.  The  Postal  Money  Order. 

2.  The  Express  Money  Order. 

3.  The  Telegraph  Money  Order. 

4.  The  Personal  Check. 

5.  The  Bank  Draft,  or  Cashier's  Check. 


EXCILINGE 


129 


I.  The  Postal  Money  Order  is  a  written  order  signed  by  the 
postmaster  in  one  place  directing  the  postmaster  in  another  place 
to  pay  to  the  person  named  in  the  order  a  specified  sum  of  money. 

A  small  fee  is  charged  for  a  postal  money  order,  the  charge 
depending  upon  the  amount  of  money  transferred.  The  follow- 
ing reproduction  of  the  table  of  rates  issued  by  the  Government 
gives  the  various  fees. 


RATES   FOR   POSTAL    MONEY   ORDERS 

From  $  0.01  to  $     2.50 *    $.03 

From  $  2.51  to  $     5.00 05 

From  $  5.01  to  $  10.00 08 

From  $10.01  to  $  20.00 10 

From  .$20.01  to  $  30.00 12 

From  $30.01  to  $  40.00 15 

From  $40.01  to  $  50.00 18 

From  $50.01  to  $  60.00 20 

From  ^60.01  to  $  75.00 25 

From  $75.01  to  $100.00 30 


For  amounts  in  excess  of  $100,  additional  orders  must  be  purchased, 
that  amount  being  the  maximum  amount  for  a  single  order. 


ORAL   PRACTICE 

Give  the  cost  of  a  postal  money  order  for : 

1.  $3.50.        4.  $9.75.        7.  $28.50.    10.  $52.50.  13.  $110.00. 

2.  $4.57.        5.  $11.75.      8.  $35.00.    11.  $74.00.  14.  $135.00. 

3.  $7.50.       6.  $21.80.      9.  $38.90.    12.  $81.91.  15.  $187.15. 

Give  the  total  amount  paid  by  the  purchaser  of  a  money  order 
for : 

16.  $11.70.    18.  $47.25.    20.  $56.15.    22.  $110.00.  24.  $142.65. 

17.  $31.50.    19.  $65.75.    21.  $75.90.    23.  $131.50.  25.  $169.90. 


130  BANKING 

n.  The  Express  Money  Order  is  similar  to  the  postal  order, 
but  the  conditions  limiting  its  payment  are  somewhat  different.  A 
postal  money  order  is  payable  to  the  party  named  in  it,  and  only 
at  the  place  named ;  while  an  express  money  order  is  payable  to 
the  order  of  the  person  named  in  it,  and  at  any  office  of  the  same 
company  where  such  orders  are  issued. 

The  rates  for  express  money  orders  up  to  fifty  dollars  are  the 
same  as  those  for  postal  money  orders.  Beyond  that  amount 
additional  orders  must  be  purchased,  the  rates  for  which  are  the 
same  as  in  the  case  of  a  similar  amount  sent  by  postal  money 
order.     For  example : 

$90  sent  by  express  money  order  would  be  sent  in  two  orders,  one  for 
$50,  the  other  for  $40.  The  rate  for  both  orders  would  be  $.30,  just  as 
much  as  if  the  whole  amount  had  been  sent  by  a  postal  money  order. 

ORAL  PRACTICE 

Give  the  cost  of  an  express  money  order  for : 

1.  $35.    3.    $60.    5.    $75.    7.    $87.50.      9.    $100.    11.   $110.50. 

2.  $45.    4.    $69.    6.    $92.    8.    $95.25.    10.    $125.    12.    $145.00. 

WRITTEN  APPLICATIONS 

1.  Compare  the  cost  of  sending  $150  by  Postal  Money  Order 
and  the  cost  of  sending  it  by  Express  Money  Order. 

2.  Find  the  total  cost  of  sending  five  express  money  orders,  the 
amounts  being,  respectively,  $12.50,  $42,  $18.75,  $31.05,  and  $29. 

3.  A  letter  may  be  registered  for  10  cents.  Compare  the  cost 
of  sending  $50  by  registered  mail  with  the  cost  of  sending  the 
same  sum  by  Postal  Money  Order. 

4.  How  much  would  a  firm  save  by  sending  $450  by  registered 
mail  instead  of  sending  it  by  Express  Money  Order?  How  much 
would  be  saved  by  sending  $450  by  Postal  Money  Order  instead 
of  by  Express  Money  Order? 


EXCHANGE 


131 


III.  The  Telegraph  Money  Order  is  issued  by  agents  of  the 
telegraph  companies,  on  a  plan  similar  to  that  of  the  postal  and 
express  orders,  and  affords  the  quickest  possible  form  of  exchange. 

The  rates  charged  for  telegraph  money  orders  include  (1)  the 
cost  of  a  fifteen  word  message  from  the  office  of  deposit  to  the 
office  of  payment,  and  (2)  a  premium  based  upon  the  following 
table. 


RATES   FOR   TELEGRAPH   MONEY  ORDERS 


For  $25.00  or  less  .  .  . 
From  $25.01  up  to  $50.00 
From  $50.01  up  to  $75.00 
From  $75.01  up  to  $100.01 


$0.25 
.35 
.60 

.85 


For  amounts  in  excess  of  $100  add  to  the  rate  for  $100  twenty-five 
cents  per  hundred  up  to  $3000.  For  amounts  in  excess  of  $3000  add 
twenty  cents  per  $100  or  fraction  of  $100. 

Illustration : 

The  rate  for  a  fifteen-word  day  message  between  Philadelphia  and 
Boston  is-  "48  and  3.5"  ;  that  is,  the  charge  is  48  cents  for  the  first  ten 
words  and  3.5  cents  for  each  word  in  excess  of  ten.  What  wiU  be  the  cost 
of  sending  $65  from  Philadelphia  to  Boston  by  telegraph  money  order? 

Rate  for  15-word  message  between  the  two  points       .     .     $  .66 

Rate  for  $65  (between  $50.01  and  $75.00) 60 

War  Tax .10 

Total  cost  for  exchange $1.36 

ORAL   PRACTICE 

With  the  15-word  message  rate  indicated  find  the  cost  of  tele- 
graph orders  for  each  amount : 

30  and  2.5:  36  and  2.5:  42  and  3.5:  60  and  3.5:  90  and  6: 

1.  $25.  6.  $40.           11.  $45.            16.  $55.  21.  $80. 

2.  $60.  7.  $90.           12.  $80.            17.  $85.  22.  $90. 

3.  $90.  8.  $150.    13.  $100.    18.  $100.  23.  $125. 

4.  $110.  9.  $225.    14.  $275.    19.  $250.  24.  $350. 

5.  $175.  10.  $300.    15.  $500.    20.  $600.  25.  $900. 


132  BANKING 

IV.  The  Personal  Check,  as  we  have  learned,  is  a  common 
form  of  exchange  in  business  transactions. 

The  personal  check  is  drawn  on  a  bank  in  which  the  person  who 
signs  it  has  a  deposit. 

The  payee  presents  it  to  his  local  bank  for  cash  or  credit. 

This  bank  collects  it  from  the  bank  on  which  it  is  drawn. 

The  collection  of  personal  checks  is  made  without  charge  when 
the  transaction  is  wholly  within  a  city  or  banking  zone  where 
both  banks  involved  transact  business.  When  a  personal  check 
is  presented  for  payment  at  some  distance  from  the  bank  upon 
which  it  is  drawn,  a  small  charge  is  made  for  collection. 

A  Certified  Check  is  a  check  upon  which  the  bank  holding 
funds  to  pay  it  makes  the  statement  that  the  sum  called  for  will 
be  held  to  meet  it.  A  certified  check  becomes,  therefore,  an 
obligation  of  the  bank  carrying  the  maker's  account. 

WRITTEN  APPLICATIONS 

1.  Write  your  personal  check  on  one  of  your  local  banks, 
payable  to  the  Western  Electric  Company,  for  one  hundred  sixteen 
dollars  and  seventy  cents. 

2.  Write  your  personal  check  on  one  of  your  local  banks, 
payable  to  John  M.  French  &  Co.,  for  two  hundred  ninety-six 
dollars,  and  indicate  the  certification  of  the  check  by  the  cashier 
of  your  bank.  (This  process  is  usually  done  by  stamping  the 
word  ''  Certified  "  and  writing  underneath  it  the  signature  of 
the  bank's  cashier  and  the  date  of  the  certification.) 

3.  Write  a  check  on  one  of  your  local  banks  payable  to  the 
Grand  Rapids  Furniture  Company  to  illustrate  the  payment  of 
twenty-five  hundred  dollars  by  one  of  your  leading  business  houses. 
Indicate  the  proper  certification  of  the  check,  and  on  the  back 
show  how  the  company  receiving  it  indorses  it  for  deposit  in  their 
local  bank. 


EXCHANGE 


133 


V.  The  Bank  Draft  is  a  check  drawn  by  one  bank  upon  another 
bank. 

In  order  to  simpHfy  the  transactions  of  business  between  differ- 
ent sections  of  the  country,  it  is  customary  for  banks  in  one 
section  to  keep  deposits  with  correspondent  banks  in  other 
sections.  Consequently,  one  bank  may  draw  checks  upon  another 
bank,  just  as  individuals  draw  their  checks  on  their  local  banks. 

Illustration : 

The  Fort  Dearborn  National  Bank  of  Chicago  keeps  a  deposit 
with  the  Chemical  National  Bank  of  New  York  City. 

Mr.  John  Brown  of  Chicago  wishes  to  pay  $300  to  Mr.  William 
Arnold  of  Philadelphia. 

Mr.  Brown,  therefore,  obtains  a  ha7ik  draft  made  out  as  follows : 


Mr.  Brown  indorses  the  check  on  the  back  thus :  "  Pay  to 
the  order  of  William  Arnold,"  and  mails  it  to  Mr.  Arnold  of 
Philadelphia.  Any  bank  in  Philadelphia  will  pay  the  $300  it 
calls  for  to  Mr.  Arnold,  or  will  credit  the  amount  to  his  account. 

Finally,  the  bank  receiving  the  draft  in  Philadelphia  will  send 
it  to  New  York  for  collection,  where,  through  the  Clearing  House, 
the  $300  will  be  paid  over  to  the  Philadelphia  bank  by  the  Chemical 
National  Bank;  and  the  Chemical  National  Bank  will  charge 
the  $300  to  the  account  of  the  Fort  Dearborn  National  Bank  w^hich 
issued  the  draft. 


134  BANKING 

VI.  The  Sight  Draft  is  a  form  of  bank  draft  by  which  exchange  is 
made  between  two  individuals,  one  of  whom  "  draws  "  upon  the 
other  to  satisfy  a  debt. 

The  working  process  is  as  follows : 

Mr.  Henry  Field  of  Chicago,  Illinois,  wishes  to  collect  $500 
from  Mr.  Wm.  Franklin  of  New  York  City.  Mr.  Field  makes 
out  the  following  draft : 

8WBBiiiiiii«iiiii>mirminiifHfttttmmi 

1E00«00  Chleago,   Illinois,   Septeml)er  10,      1'l,>0fl  Q 

At  Sight TPr^^ynTfflTR 

OPjTTlSTt^j     CHEMICAL  glTIOHAL  BAHZ  of  Hew  Yort 

rive  Haadred -j  1"^  (TKl-^^cryt 

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The  local  bank  where  Mr.  Field  transacts  his  business  cashes 
this  draft  and  pays  the  amount  to  him,  less  a  small  fee  charged 
for  exchange. 

The  Chemical  National  Bank  collects  the  amount  from  its 
correspondent  bank  in  New  York  and  pays  it  over  to  the  Chicago 
bank  that  paid  the  sum  to  Mr.  Field. 

If  Mr.  Franklin  refuses  to  pay  the  draft  the  New  York  bank 
returns  it  to  the  Chemical  National  Bank,  and  this  latter  bank 
notifies  the  Chicago  bank  that  payment  is  refused.  The  Chicago 
bank  immediately  notifies  Mr.  Field  that  he  must  "  take  up  the 
draft,"  that  is,  refund  the  money  that  they  paid  him. 

If  Mr.  Franklin  pays  the  draft  the  transaction  closes  when  the 
New  York  bank  remits  to  the  Chemical  National  Bank  the  amount 
that  they  have  advanced  to  the  Chicago  bank. 


EXCHANGE  135 

If  Mr.  Franklin's  indebtedness  to  Mr.  Field  is  not  due  for  ninety 
days,  the  draft  would  have  been  written  with  the  words  "  Ninety 
days  after  sight,"  instead  of  "  at  sight."  Mr.  Frankhn  then  has 
the  privilege  of  indorsing  the  draft  with  the  word  ''  Accepted  " 
across  the  face,  signing  his  name  underneath;  this  process  con- 
verting the  draft  to  an  ''  acceptance  "  which  is  virtually  a  promis- 
sory note  due  ninety  days  after  the  date  of  acceptance. 

APPLICATIONS   OF  EXCHANGE  BY  BANK  DRAFTS 

We  have  found  that  the  exchange  of  money  by  Postal  or  Ex- 
press Orders  is  made  at  a  small  cost  dependent  upon  the  amount 
of  money  transferred.  It  is  also  true  that  exchange  by  bank 
draft  may  require  a  small  expense,  but,  on  the  other  hand,  a 
saving  is  possible  under  certain  conditions. 

The  demand  for  money  in  one  citj'  may  be  limited  while  the  supply 
may  be  abundant.  In  another  city  the  demand  may  be  great  but  the 
supply  limited.  Consequently,  the  rate  of  exchange  between  the  two 
cities  will  be  affected,  and  the  city  which  is  in  need  of  money  will  be  made 
to  pay  a  certain  additional  percentage  in  order  to  get  it. 

If  New  York  has  a  large  demand  for  drafts  on  Chicago,  but  Chicago 
has  only  a  hmited  demand  for  drafts  on  New  York,  the  supply  of  cash 
on  deposit  in  Chicago  by  New  York  banks  will  be  exhausted.  As  a  check 
upon  such  a  situation  the  rate  for  New  York  Exchange  on  Chicago  will 
rise,  and  at  the  same  time  the  rate  for  Chicago  Exchange  on  New  York 
will  faU. 

The  Rate  of  Exchange  is  usually  quoted  as  a  number  of  cents 
per  $1000  transferred. 

In  problems  of  exchange  we  must  consider 

(a)  The  amount  to  be  transferred,  and 

(6)  The  value  of  money  in  one  place  compared  with  the  value  in  the 
other  place,  or  the  rate  of  exchange. 

Because  of  the  expense  of  maintaining  facilities  for  the  transfer  of 
money,  most  banks  charge  a  small  fee  for  a  draft.  Many  banks,  how= 
ever,  do  not  ask  this  fee  from  their  regular  depositors. 


136  BANKING 

Exchange  Quotations. 

If  the  cost  of  exchange  is  added  to  the  amount  transferred,  ex- 
change is  said  to  be  at  a  Premium. 

If  the  cost  of  exchange  is  deducted  from  the  amount  transferred, 
exchange  is  said  to  be  at  a  Discount. 

If  there  is  neither  a  premium  nor  a  discount,  exchange  is  said  to 
be  at  Par. 

To  Find  the  Cost  of  a  Draft 

Ilhistration : 

1.  At  i%  premium  find  the  cost  of  a  draft  for  $5000. 

■^%  premium  means  -^  of  1%  of  $5000. 

i  of  1%  of  $5000  =  .5  of  .01  of  $5000  =  .005  X  $5000  =  $25. 
$5000 +$25  =  $5025,  the  cost  of  a  draft  for  $5000. 

2.  Find  the  cost  of  a  draft  for  $2500  when  exchange  is  selhng 
at  50  cents  discount. 

50  cents  discount  means  50  cents  discount  on  each  $1000. 
The  discount  on  $2500,  or  2.5  thousands,  is  2.5  X$.50  =  $1.25. 
$2500  -$1.25  =  $2498.75,  the  cost  of  a  draft  is  for  $2500. 

WRITTEN  APPLICATIONS 

Find  the  cost  of  a  draft  for 

1.  $2000  at  20  cents  premium. 

2.  $2000  at  20  cents  discount. 

3.  $3000  at  30  cents  premium. 

4.  $5000  at  50  cents  discount. 

5.  $4000  at  75  cents  premium. 

6.  $1000  at  i%  premium. 

7.  $1500  at  f  %  discount. 

8.  $2000  at  i%  discount. 

9.  $3500  at  .001  discount. 

10.  $6000  at  .0015  discount. 

11.  What  is  the  cost  of  a  draft  on  San  Francisco  for  $4500,  if 
the  rate  of  exchange  is  i%  discount  ? 


EXCHANGE  137 

12.  A  mercnant  in  Philadelphia  owes  S3000  to  a  wholesale  firm 
in  Chicago.  How  much  must  he  pay  for  a  draft  for  the  sum,  if 
exchange  is  f  %  premium  ? 

13.  Find  the  total  amount  that  must  be  paid  to  a  bank  for  a 
draft  of  $4000,  if  the  exchange  rate  is  75  cents  premium,  and  a  fee 
of  50  cents  is  charged  by  the  bank  for  the  transfer. 

14.  Find  the  total  amount  that  must  be  paid  to  a  bank  for  a 
draft  of  $4000,  if  the  exchange  rate  is  75  cents  discount,  and  a  fee 
of  $1.00  is  charged  by  the  bank  for  the  transfer. 

15.  A  merchant  in  Chicago  draws  on  another  in  Philadelphia, 
the  face  of  the  draft  being  $4500.  If  the  exchange  rate  is  ^% 
discount,  what  is  the  amount  received  by  the  Chicago  merchant  ? 

16.  A  merchant  owes  $2000  to  a  wholesale  firm  in  New  York. 
How  much  will  he  save  if,  instead  of  sending  his  check,  he  pur- 
chases a  draft  in  which  the  exchange  rate  is  75  cents  discount? 

17.  A  draft  on  San  Antonio  was  purchased  in  Boston  when 
exchange  was  50  cents  premium.  If  $10,000  was  transferred, 
how  much  did  the  exchange  and  the  face  of  the  draft  cost  the 
sender  ? 

18.  A  merchant  in  New  Orleans  bought  a  bill  of  goods  in  Chicago 
amounting  to  $12,500,  on  which  the  discounts  were  15%  and  10%. 
If  he  paid  for  the  goods  mth  a  draft  on  which  the  discount  was  i%, 
find  the  sum  he  remitted  to  Chicago. 

19.  In  making  advance  payment  for  a  bill  of  goods  amounting 
to  $10,600,  a  merchant  transferred  the  money  by  telegraph.  If 
the  premium  on  the  exchange  was  75^,  and  if  the  cost  of  the  tele- 
graph transfer  was  $22.30,  how  much  did  the  merchant  pay  out  on 
the  whole  transaction  ? 

20.  A  merchant  paid  two  bills  by  buying  drafts.  One  of  them 
called  for  $2700  in  a  city  on  which  the  exchange  rate  was  30  cents 
premium,  and  the  other  for  $5600  in  another  city  on  which  the 
exchange  rate  was  f%  discount.  How  much  did  both  drafts 
f'^st'f  How  much  did  he  save  by  buying  the  drafts  instead  of 
using  his  personal  checks? 


138 


RATIO  AND  PROPORTION 


RATIO  AND  PROPORTION 

RATIO 

A  Ratio  is  the  quotient  of  one  quantity  divided  by  another, 
both  being  of  the  same  kind. 

Thus  :     The  ratio  of  3  to  6  is  3^6,  or  f . 
The  ratio  of  6  to  3  is  6-4-3,  or  f. 

The  quotient  of  one  number  divided  by  another  number  of  the 
same  kind  is  always  an  abstract  number,  hence, 

All  ratios  are  abstract  numbers. 

The  ratio  of  two  numbers  is  often  expressed  by  using  the  Ratio 
Sign  ( : ) 

Thus  :     The  ratio  of  3  to  6  may  be  expressed  3  :  6. 

The  first  number  of  a  ratio  is  the  Antecedent.     The  second 
number  is  the  Consequent. 

Thus :    In  the  ratio  5  :  7,  which  is  read  "Five  to  seven," 
The  antecedent  is  5,  and  the  consequent  is  7. 

The  Terms  of  a  Ratio  are  the  antecedent  and  consequent  of 
that  ratio. 

ORAL  PRACTICE 

Expressing  both  measures  in  the  same  kind  of  unit,  give  the 
ratio  of : 


1.  1  inch  to  1  foot. 

2.  1  foot  to  1  yard. 

3.  1  foot  to  1  mile. 

4.  1  ounce  to  1  pound. 

5.  1  hour  to  1  day. 

6.  1  second  to  1  hour. 

7.  1  minute  to  1  day. 


8.  1  foot  to  1  inch. 

9.  1  mile  to  1  yard. 

10.  1  hour  to  1  minute. 

11.  1  gallon  to  1  pint. 

12.  1  bushel  to  1  quart. 

13.  1  week  to  1  year. 

14.  1  cu.  ft.  to  1  cu.  yd. 


RATIO  139 

APPLICATIONS    OF   RATIOS 

I.   To  change  the  form  of  a  ratio,  or  to  reduce  its  terms  with- 
out changing  their  ratio. 

Since  a  ratio  may  be  expressed  as  a  fraction  it  follows  that 

The  terms  of  a  ratio  may  he  multiplied  by,  or  may  he  divided  by, 
the  same  number  without  changing  the  value  of  the  ratio. 

Illustration : 

1.  Find  the  ratio  of  15  to  20. 

1  r  .  on  _  iS.  _  3. 
xo  .  ^u       2  0       T' 

That  is,  the  ratio  of  15  to  20  is  the  same  as  the  ratio  of  3  to  4, 
Illustration : 

2.  Find  the  ratio  of  If  to  1^. 

To  change  to  whole  numbers  multiply  each  term  of  the  ratio  by  12, 
the  L.  C.  M.  of  the  denominators. 

If      HX12      20      4       „      , 

4  4 

That  is,  the  ratio  of  If  to  l^^^  is  the  same  as  the  ratio  of  4  to  3. 

BLACKBOARD  PRACTICE 

Give,  in  simplest  form,  the  ratio  of : 

1.  4  to  8.  8  to  4.  6  to  12.  12  to  6.  6  to  9. 

2.  8  to  12.  8  to  16.  8  to  20.  12  to  15.  12  to  18. 

3.  10  to  5.  10  to  6.  12  to  8.  12  to  20.  16  to  20. 

4.  16  to  4.  20  to  6.  20  to  5.  20  to  24.  20  to  30. 

5.  30  to  45.  40  to  60.  45  to  60.  55  to  60.  24  to  72. 

6.  itof.  itof.  itof.  f  tof.  f  to^. 

7.  itoi.  f  to^^.  f  tof.  f  tof.  ftoif. 

8.  .4  to  .7.  .5  to  .9.  .15  to  .9.  .3  to  6.  1.5  to  7.5. 

9.  l.n  to  5.  .05  to  .1.  .75  to  30.  12.5  to  .625.  .18  to  14.4. 


140  RATIO  AND  PROPORTION 

II.   To  separate  a  number  into  parts  that  shall  have  a  ratio 
equal  to  a  given  ratio. 

Illustration : 

Divide  a  line  100  feet  long  into  parts  that  shall  have  the  ratio 
of  2  to  3. 

For  each  2  feet  in  one  part  there  will  be  3  feet  in  the  other  part. 
And  each  portion  2  feet  long  plus  each  corresponding  portion  3  feet 
long  together  make  a  length  5  feet  long. 

Hence,  one  part  of  the  100  feet  will  be  f  of  the  whole,  and  the  other 
part  of  the  100  feet  will  be  f  of  the  whole, 
f  of  100  ft.  =40  ft.,  one  part, 
|-  of  100  ft.  =60  ft.,  the  other  part.     Result. 
The  result  is  readily  proved,  for  40  :  60  =  |^^  =|-. 

BLACKBOARD   PRACTICE 

Separate 

1.  36  in  the  ratio  of  1  to  3.  7.  150  in  the  ratio  of  6  to  19. 

2.  45  in  the  ratio  of  4  to  5.  8.  200  in  the  ratio  of  7  to  13. 

3.  75  in  the  ratio  of  7  to  8.  9.  208  in  the  ratio  of  4  to  9. 

4.  110  in  the  ratio  of  4  to  7.  10.  264  in  the  ratio  of  6  to  11. 

5.  140  in  the  ratio  of  3  to  7.  11.  324  in  the  ratio  of  10  to  19.. 

6.  165  in  the  ratio  of  5  to  11.  12.  500  in  the  ratio  of  12  to  29 

WRITTEN   APPLICATIONS 

1.  In  mixing  the  grades  of  coffee  a  grocer  puts  in  60  pounds  of 
one  kind  and  40  pounds  of  another  kind.  What  is  the  ratio  of 
the  amount  of  the  first  kind  to  the  amount  of  the  second  kind  ? 

2.  In  a  certain  fertilizer  a  farmer  uses  875  pounds  of  acid 
phosphate  and  175  pounds  of  kainit.  What  is  the  ratio  of  the 
phosphate  to  the  kainit  ? 

3.  A  contractor  uses  35  bags  of  cement  and  5  cubic  yards  of 
crushed  stone  for  a  concrete  floor.  If  a  bag  of  cement  is  equiva- 
lent to  1  cubic  foot,  what  is  the  ratio  of  this  amount  to  the  amount 
of  crushed  stone  used  ? 


RATIO  141 

4.  A  fruit  grower  has  on  hand  150  pounds  of  copper  sulphate, 
and  in  the  spray  he  plans  to  use  he  must  have  sufficient  lime  to 
make  the  ratio  of  the  sulphate  to  the  lime  2  to  7.  How  many- 
pounds  of  lime  must  he  use? 

5.  A  fertilizer  used  for  market  gardening  contains  2500  pounds 
of  nitrate  of  soda,  and  the  ratio  of  this  nitrate  to  the  acid  phos- 
phate in  the  mixture  must  be  8  to  5.  How  many  pounds  of  acid 
phosphate  must  be  used  ? 

6.  Two  men  rented  a  roller  and  paid  S60  for  its  use.  One 
man  used  it  9  days  and  the  other  man  used  it  21  days.  How  much 
should  each  man  pay? 

7.  A  farmer  finds  that  the  ratio  of  the  butter  fat  to  the  milk 
produced  by  his  herd  is  1  to  25.  At  this  rate  how  many  pounds 
of  butter  fat  are  produced  at  one  milking,  if  his  20  cows  average 
18  pounds  of  milk  each? 

8.  One  man  invests  $3000  and  another  $4200  in  a  business, 
and  the  profit  of  this  business  amounts  to  $4800.  Divide  this 
profit  into  two  shares  that  shall  be  in  the  same  ratio  as  the  amounts 
each  man  invested. 

9.  An  estate  is  so  divided  that  the  only  child  receives  $2  for 
every  $5  left  to  the  widow.  If  the  total  value  of  the  property  is 
$37,500,  find  the  amount  each  of  the  two  heirs  receives. 

10.  Two  merchants  bought  a  carload  of  coal  weighing  100,000 
pounds.  One  of  them  took  30  tons  of  it,  and  the  other  took  the 
rest  of  it,  each  taking  2000  pounds  to  the  ton.  The  freight  was 
$.60  per  ton.  Find  the  amount  of  freight  that  each  should  pay, 
ii  they  divide  the  freight  in  the  same  ratio  as  they  divided  the 
coal. 


142  RATIO  AND  PROPORTION 

PROPORTION 

A  Proportion  is  an  expression  of  equality  between  two  ratios. 

Thus  :  4 :  8  =  5  :  10  is  a  proportion. 

The  same  proportion  may  be  expressed  q  =  77;- 

o     lU 

This  proportion  is  read 

"The  ratio  of  4  to  8  is  equal  to  the  ratio  of  5  to  10,*' 

Or,  briefly, 

"4  is  to  8  as  5  is  to  10." 

The  Extremes  of  a  Proportion  are  the  first  and  fourth  terms, 
4  and  10  are  the  extremes  of  the  proportion  given  above. 

The  Means  of  a  Proportion  are  the  second  and  third  terms. 
8  and  5  are  the  means  of  the  proportion  given  above. 

In  the  proportion 

4:8=5:10, 
It  will  be  observed  that  4  X 10  =  40, 
and  also  that  8X5=40.     That  is, 

The  product  of  the  means  is  equal  to  the  product  of  the  ex- 
tremes. 

This  principle  may  be  proved  true  for  any  proportion. 
If  the  pupil  requires  a  proof  the  following  will  convince. 

The  proportion  4:8=5:10 

4      5 

may  be  written  0=  tK 

o      10 

Multiplying  each  member  of  the  equation  by  8X10  we  have 

8X10X4      8X10X5 
8  10       * 

Canceling  **8"  from  the  left  member,  and  "10"  from  the  right  mem^^ 
ber,  we  have 

10X4=8X5. 

The  pupil  should  go  through  the  same  process  with  some  other  pro- 
portion. 


PROPORTION  143 

By  this  principle  we  may  find  any  missing  term  of  a  proportion  when 
three  terms  are  known. 

In  a  proportion  as,  for  example,  6  :  9  =  10  :  15, 

We  have  6X15=9X10. 

Dividing  both  members  by  one  extreme  (6),  - — ^— ^=  — -^ — 

o  o 

9X10 
Canceling  the  6  in  the  left  member,  15  =  — ^ — ■• 

Or,  dividing  both  members  by  the  other  extreme  (15), 

6X15     9X10 


15  15 

9X10 
Canceling  the  15  in  the  left  member,  6  =  — 7^-* 

lo 

In  general,  therefore, 

Either  extreme  of  a  proportion  is  equal  to  the  product  of  the 
means  divided  by  the  other  extreme. 

By  dividing  both  members  by  either  mean  it  may  be  shown  that 

Either  mean  of  a  proportion  is  equal  to  the  product  of  the  ex- 
tremes divided  by  the  other  mean. 

Illustrations : 

1.  Given  8  :  12  =  4  :  x.   Find  x.     2.  Given  7  :  a:  =  10 :  30.   Find  x. 

8  re  =48.  10  X  =210. 

x=6.     Result.  '  x=21.     Result. 

BLACKBOARD   PRACTICE 

In  each  of  the  following  proportions  find  the  value  of  the  un- 


known  term : 

1. 

a;:6  =  8:  16. 

8. 

/>. .  2  _  3  .  1 

U/  .  3-  — ^  .   2-. 

2. 

0^:7  =  4:14. 

9. 

3    .    /y.  2.5 

4"  '  **'        3^  •   6' 

3. 

5:  0^  =  4:12. 

10. 

7  .    1—^.8 

4. 

9:x=.8:24. 

11. 

3   .   5 1  2   .  /v. 

5. 

a::  12  =  10:  15. 

12. 

0.2  :a:  =  0.15:  0.03. 

6. 

10:a:  =  9:12. 

13. 

0.5:  1.5  =  x:0.06. 

7. 

12:  18  =  x:  15. 

14. 

a: :  2.5  =  0.75:  0.625 

144  RATIO  AND  PROPORTION 

Practical  Uses  of  Proportion  in  Business.  Many  problems 
occurring  in  every-day  business  practice  are  readily  solved  by 
the  use  of  proportion. 

Illustration : 

If  12  barrels  of  flour  cost  ^69,  how  much  will  21  barrels  of  flour 
cost  ? 

We  make  up  our  proportion  by  (1)  placing  quantities  of  the  same  kind 
together  in  our  ratios,  and  (2)  by  observing  that  a  small  number  of  barrels 
is  the  first  term  of  one  ratio,  and  a  small  number  of  dollars  is  the  first  term 
of  the  second  ratio.     That  is, 

small  no.  bbl. :  large  no.  bbl.  =  small  no.  dollars  :  large  no.  dollars. 

The  proportion  is,  then,     12  :  21  =S69  :  $x. 

Whence,  x  = — r^ — 

Solving,  X  =  120^. 

But  the  second  ratio  is  an  expression  in  dollars,  hence,  the  result  is  a  num- 
ber of  dollars.     Therefore,  the  cost  of  21  barrels  will  be  $120.75.     Result. 

In  certain  types  of  problems  care  must  be  taken  to  observe 
the  order  in  which  the  ratios  are  expressed.  Problems  involving 
labor  illustrate  this  type. 

Illustration : 

If  10  men  can  complete  a  task  in  9  days,  how  many  days  will  it 
take  15  men  to  do  the  same  work? 

Increasing  the  number  of  men  will  shorten  the  time  required,  hence, 
large  no.  men :  small  no.  men  =  large  no.  days  :  small  no.  days. 

The  proportion  is,  then,     15  :  10  =  9  :  x. 
From  which,  x=6. 

That  is,  15  men  will  do  the  work  in  6  days.     Result. 

In  all  problems  in  proportion  the  words  "  at  the  same  rate  " 
are  always  understood.  Proportion  is  frequently  used  in  the  work 
of  later  mathematics,  and  this  simple  treatment  should  be 
thoroughly  understood. 


PROPORTION  145 

WRITTEN   APPLICATIONS 

Proportion  Applied  to  Business 

1.  If  5  chains  cost  $15,  what  will  9  chains  cost? 

2.  If  6  books  cost  $21,  what  will  10  books  cost? 

3.  If  9  chairs  cost  $36,  what  will  15  chairs  cost? 

4.  If  12  watches  cost  $96,  what  will  20  watches  cost? 

5.  If  15  sheets  cost  $12,  what  will  48  sheets  cost? 

6.  If  18  pairs  of  shoes  cost  $54,  what  will  45  pairs  cost? 

7.  If  20  clocks  cost  $110,  what  will  29  clocks  cost? 

8.  If  12  stick  pins  cost  $o0,  what  will  56  stick  pins  cost  ? 

9.  If  15  mattresses  cost  $112.50,  what  will  21  mattresses  cost  ? 

10.  A  dealer  paid  $412.50  for  11  rugs.  How  much  should  he 
-psLj  for  17  such  rugs? 

11.  A  dealer  in  clothing  bought  12  dresses  for  $219.  How  much 
should  he  pay  for  23  dresses  of  the  same  kind  ? 

12.  A  bicycle  manufacturer  sold  13  bicycles  for  $327.60,  and 
later  he  sold  27  more  at  the  same  price  apiece.  What  amount 
did  he  receive  for  the  second  lot  ? 

13.  A  laborer  was  paid  $16.80  for  8  days'  work.  How  much 
should  he  receive  for  working  13  days? 

14.  45  M  feet  of  lumber  cost  a  dealer  $990,  and  later  he  bought 
24  M  feet  more  of  the  same  kind  of  lumber.  How  much  did  he 
pay  for  the  second  lot  at  the  same  rate? 

15.  An  automobile  runs  16  miles  in  30  minutes.  At  the  same 
rate,  how  many  miles  will  it  run  in  one  and  one  quarter  hours? 

16.  A  dealer  in  provisions  paid  $5.76  freight  charges  on  18  cases 
of  eggs.     At  this  rate,  how  much  was  the  freight  charge  on  33  cases  ? 

17.  For  the  cost  of  delivering  80  tons  of  coal  a  dealer  paid  $35. 
At  this  rate  how  much  should  he  charge  for  delivering  15  tons  to 
another  customer? 

18.  In  350  pounds  of  milk  there  are  13.3  pounds  of  butter  fat. 
At  this  rate,  how  much  butter  fat  should  there  be  in  1000  pounds 
of  milk? 


146  RATIO  AND  PROPORTION 

19.  A  machine  makes  250  bolts  in  one  and  one  quarter  hours. 
How  many  bolts  will  this  machine  make  in  55  hours  ? 

20.  A  cleaning  establishment  charged  $2.16  for  cleaning  a  rug 
9  feet  long  and  6  feet  wide.  How  much  will  they  charge,  at  the 
same  rate,  for  cleaning  a  rug  10  feet  long  and  8  feet  wide? 

21.  A  parquet  floor  16  feet  long  and  12  feet  wide  is  laid  at  a  cost 
of  $38.40.  How  much  will  it  cost,  at  the  same  rate,  to  lay  such  a 
floor  in  a  room  18  feet  long  and  15  feet  wide,  and  in  a  hallway 
18  feet  long  and  9  feet  wide? 

22.  A  farmer  finds  that  80  bushels  of  grain  is  sufficient  to  feed 
his  herd  of  cows  for  one  week  if  each  cow  gets  4  quarts  a  day. 
If  he  changes  his  plan  so  as  to  feed  each  cow  5  quarts  daily,  how 
many  days  will  the  80  bushels  last  ? 

23.  A  practical  cattleman  feeds  3  pounds  of  hay  at  a  feeding 
for  each  100  pounds  of  live  weight  of  his  herd.  At  that  rate  what 
amount  should  he  feed  to  a  steer  weighing  1250  pounds?  What 
amount  should  he  feed  to  one  weighing  900  pounds? 

Proportion  Applied  to  Problems  Involving  Time 

24.  If  12  men  can  complete  a  task  in  10  days,  how  many  days 
will  it  take  15  men  to  complete  the  same  task? 

25.  12  men  built  a  section  of  a  wall  in  9  days.  How  many 
days  would  it  take  18  men  to  build  such  a  section? 

26.  26  men  can  complete  a  concrete  pavement  in  12  days,  but 
only  8  men  are  put  at  the  work.  How  many  days  will  it  take 
these  8  men  to  complete  it  ? 

27.  32  women  can  pick  all  of  the  strawberries  in  a  strawberry 
bed  ui  30  hours.  How  many  women  will  it  take  to  pick  them  in 
20  hours? 

28.  A  farmer  had  enough  feed  to  supply  his  27  cows  for  72 
days,  but  he  sold  9  of  them.  How  many  days  will  this  feed  supply 
the  rest  of  his  cows  ? 


PROPORTION  147 

29.  A  herd  of  75  head  of  cattle  will  consume  a  certain  amount 
of  grain  in  9  days,  but  the  owner  adds  30  head  to  the  herd.  How 
many  days  will  this  grain  last? 

30.  50  men  were  engaged  to  work  upon  a  paving  job  which 
they  could  fmish  in  25  days,  but  5  of  them  failed  to  report  for 
work.     How  long  should  it  take  the  others  to  do  the  work? 

31.  100  men  were  building  a  highway  which  they  could  finish 
in  12  days.  If  20  of  them  gave  up  the  work,  how  long  should  it 
take  the  others  to  complete  it  ? 

32.  120  men  can  complete  a  paving  job  in  15  days,  but  the  con- 
tractor wishes  to  finish  the  work  in  10  days.  How  many  more 
men  must  he  employ  to  do  this  ? 

33.  A  farmer  has  on  hand  a  supply  of  grain  that  will  feed  46 
cows  for  the  three  months  of  November,  December,  and  January. 
If  he  sells  10  cows,  how  many  days  will  the  feed  last  for  those  that 
he  keeps? 

34.  A  contractor  has  100  days  in  which  to  build  a  wall,  and  he 
has  12  men  to  do  the  work.  If  he  should  decide  to  use  15  men, 
in  how  many  days  should  he  be  able  to  complete  the  work? 

35.  A  builder  agrees  to  complete  a  gymnasium  in  150  days,  and 
plans  to  have  an  average  of  30  men  at  work  on  it  daily  during  that 
time.  If  he  begins  10  days  late,  how  many  men  should  he  add  to 
his  force  in  order  to  complete  the  work  at  the  end  of  the  specified 
time  ? 

36.  30  linemen  can  build  a  telephone  line  in  9  days,  but  the 
contractor  has  only  4  days  in  which  to  do  the  work.  How  many 
additional  men  must  be  put  to  work  in  order  to  complete  the  line 
on  time? 

37.  A  contractor  agrees  to  decorate  the  interior  of  a  building, 
and  to  complete  the  work  in  36  working  days.  He  is  delayed 
4  days,  however,  before  beginning.  How  many  men  must  he 
put  upon  the  work  in  order  to  complete  it  in  32  days,  if  48  men 
could  have  completed  it  in  36  days? 


148 


POWERS 


POWERS 
A  Power  is  a  product  obtained  by  using  a  given  number  a  cer- 


tain number  of  times  as  a  factor. 

Thus:    2X2=4.         2X2X2=8. 
And  4,  8,  and  16  are  powers  of  2. 

Similarly:  5X5=25. 

3X3X3=27. 


2X2X2X2  =  16.     Etc. 

25  is  a  power  of  5. 
27  is  a  power  of  3. 


A  Square  is  a  power  obtained  by  using  a  number  twice  as  a 

factor. 

Thus  :     The  square  of  5  is  obtained  from  the  product  of  5  X5. 
That  is  :  5  X5  =25.     25  is  the  square  of  5. 

A  Cube  is  a  power  obtained  by  using  a  number  three  times  as 

a  factor. 

Thus  :     The  cube  of  5  is  obtained  from  the  product  of  5  X5  X5. 
That  is :  5X5X5  =  125.     125  is  the  cube  of  5. 

The  product  of  2X2  may  be  indicated  by  writing  2^. 

22  is  read  "two  squared."    2^  =4. 

Similarly  :     2X2X2  may  be  indicated  bj^  writing  2^ 

23  is  read  "two  cubed."        2^  =8. 
Also:  3X3X3  or  3^=27. 

5X5  or  52=25. 

The  small  figure,  placed  at  the  right  of  and  a  little  above  the 
number,  indicates  the  number  of  times  the  given  number  is  to  be 
used  as  a  factor,  and  is  called  an  Exponent. 

The  Relation  of  the  Square  to  the  Cube  is  readily  illustrated  by 
reviewing  our  knowledge  of  an  area  and  also  of  a  volume. 


A  square  whose 
side  is  3  units  con- 
tains (3X3)  square 
units,  or  9  square 
units  of  area. 


A  cube  whose 
edge  is  3  contains 
(3X3X3)  cubic 
units,  or  27  cubic 
units  of  volume. 


The  square  of  a  number  is  often  called  the 
Second  Power  of  the  number. 


POWERS 


149 


The  cube  of  a  number  is  often  called  the  Third  Power  of  the 
number. 

In  like  manner  we  may  speak  of  the  fourth,  the  fifth,  the  sixth 
power,  etc. 

The  following  table  should  be  memorized. 

POWERS 


22=   4 

102  =  100 

182=324 

23=     8 

32=   9 

112  =  121 

192=361 

33=   27 

42  =  16 

122  =  144 

202=400 

43=   64 

52=25 

132  =  169 

212=441 

53  =  125 

62=36 

142  =  196 

222=484 

63=216 

72=49 

152=225 

232=529 

73=343 

82=64 

162=256 

242=576 

83=512 

92=81 

172=289 

252=625 

93=729 

To  Find  the  Power  of  a  Fraction. 

Since  the  square  of  a  fraction  is  the  product  of  the  fraction  by 
itself  we  have,  And  for  the  cube 


(r= 


2  2_2X2_4 

3  3      3X3      9" 


(!r=!x! 


3  3^3X3X3^27.     ^tc. 

4  4      4X4X4      64 


That  is,  the  square  of  a  fraction  equals  the  square  of  the  numera- 
tor divided  by  the  square  of  the  denominator ; 

And,  the  cube  of  a  fraction  equals  the  cube  of  the  numerator 
divided  by  the  cube  of  the  denominator. 

The  same  principle  applies  to  powers  higher  than  the  cube. 

To  Find  a  Power  of  a  Decimal. 


(2.5)2  =  2.5X2.5=6.25. 

(1.2)3  =  1.2X1.2X1.2  =  1.728.     Etc. 

A  power  of  a  decimal  is  obtained  by  multiplication  as  in  decimals, 
care  being  exercised  in  the  proper  point  in  g-ofP  of  the  product. 


1. 

26^. 

2. 

352. 

3. 

422. 

4. 

542. 

5. 

652. 

Fin 

d  the  i 

21. 

15  m 

22. 

24  in 

23. 

30  ft. 

24. 

35  ft. 

25. 

42  ft. 

2 


150  ROOTS 

BLACKBOARD   PRACTICE 

Find  the  required  power  in  each  of  the  following : 

6.  152.  11.    (i)2.  16.  (2.5)2. 

7.  2P.  12.    (1)2.  17.  (3.15) 

8.  252.  13.    (f)-^  18.  (4.01)^ 

9.  302.  14^    (2)3^  19_  (2.15)2. 

10.   452.  15.    (1)-^  20.    (3.25)1 

Find  the  area  of  a  square  whose  side  is : 

26.  50  ft.  31.    10  ft.  6  in.  36.  10  yd.  1  ft. 

27.  50  yd.        32.    15  ft.  3  in.  37.  12  yd.  2  ft. 

28.  50  rd.         33.    18  ft.  8  in.  38.  15  yd.  1  ft. 

29.  65  yd.        34.    20  ft.  6  in.  39.  18  yd.  2  ft. 

30.  75  rd.         35.   24  ft.  3  in.  40.  20  yd.  2  ft. 

Find  the  volume  of  a  cube  whose  edge  is : 

41.  6  in.  44.   9  ft.  47.    1  ft.  6  in.  50.  3  ft.  6  in. 

42.  10  in.         45.    12  ft.  48.    1  ft.  3  in.  51.  5  ft.  9  in. 

43.  16  in.         46.    20  ft.  49.    2  ft.  6  in.  52.  8  ft.  6  in. 

ROOTS 

A  Root  of  a  number  is  one  of  the  equal  factors  of  that  number. 
A  Square  Root  of  a  number  is  one  of  the  two  equal  factors  of 
that  number. 

Thus  :        3  is  the  square  root  of  9.  (For      9  =3  X3.) 

12  is  the  square  root  of  144.     (For  144  =  12  Xl2.) 

A  Cube  Root  is  one  of  the  three  equal  factors  of  a  number. 

Thus  :         2  is  the  cube  root  of  8.  (For      8  =2x2X2.) 

4  is  the  cube  root  of  64.  (For    64  =  4  X4  X4.) 

5  is  the  cube  root  of  125.         (For  125  =5  X5  X5.) 

The  symbol  for  square  root  is  the  Radical  Sign,  V- 


ROOTS  151 

A  small  figure,  called  the  Index,  is  written  in  the  radical  sign  to 
show  what  root  or  factor  is  required.     Thus  : 

2/ — " 

v25  means  "What  is  the  square  root  of  25?"     2  is  the  index. 
v27  means  "What  is  the  cube  root  of  27?"     3  is  the  index. 

It  is  not  customary  to  write  the  index  when  a  square  root  is 
required.     Thus : 

2/ •  / 

vl6  is  the  same  as  vl6. 

Square  Root  Obtained  by  Factoring 

By  separating  a  number  into  its  prime  factors  we  are  able  in 
many  cases  to  find  its  square  root  by  inspection. 

Thus:  144=2X2X2X2X3X3. 

In  the  factors  we  find  four  2's  and  two  3's. 
Hence,  we  may  group  the  2's  in  pairs  and  write 

144  =  (2X2)X(2X2)X(3X3). 

Since  finding  square  root  is  finding  one  of  two  equal  factors,  we  may 
select  one  factor  from  each  pair  for  the  square  root  of.  that  particular  pair. 

The  product  of  the  single  factors  selected  will  be  the  square  root  of 
the  given  number,  that  is  : 

Vlii  =  2X2X3  =  12.     Result. 

By  a  similar  process  we  may  often  find  the  cube  root  of  a  number 

BLACKBOARD    PRACTICE 

By  factoring  find  the  square  root  of : 

1.  225.  5.  784.  9. 

2.  324.  6.  961.  10. 

3.  576.  7.  1024.  11. 

4.  729.  8.  1089.  12. 

Find  the  number  of  feet  in  the  side  of  the  square  whose  area  is  : 

17.  484  square  feet.  21.  729  square  yards.  . 

18.  676  square  feet.  22.  784  square  yards. 

19.  900  square  feet.  23.  3025  square  rods. 

20.  961  square  feet.  24.  4090  square  rods. 


1225. 

13. 

2304. 

1296. 

14. 

2500. 

1764. 

15. 

3136. 

2025. 

16. 

4096. 

152  ROOTS 

THE   GENERAL   METHOD   OF  FINDING   SQUARE  ROOT 
The  Relation  between  the  number  of  figures  in  a  square  and 
the  number  in  the  corresponding  square  root  may  be  shown  thus : 

The  largest  number  having  one  figure  is  9.  9^  =         81. 

The  largest  number  having  two  figures  is  99.  99^  =     9801. 

The  largest  number  having  three  figures  is  999.      999^  =998001. 

That  is : 

(1)  A  number  having  one  figure  rnay  have  as  many  as  two  figures 
in  its  square. 

(2)  A  number  having  two  figures  may  have  as  many  as  four  figures 
in  its  square. 

(3)  A  number  having  three  figures  may  have  as  many  as  six  figures 
i?i  its  square.     Etc. 

If,  therefore,  a  number  is  considered  as  "  separated  into  periods 

of  two  figures  each,"  the  number  of  such  periods  obtained  will 

equal  the  number  of  figures  in  the  square  root  which  is  sought. 

For  example  :     998001  written  thus,  99  80  01,  gives  three  periods, 
and  its  square  root,  999,  has  three  figures. 

The  period  at  the  extreme  left  need  have  but  one  figure. 

For  example:        1252  =  15625. 

15625  =  written  1  56  25  gives  three  periods, 
and  its  square  root  125  has  three  figures. 

Separating  into  periods  is  begun  at  the  decimal  point. 

The  actual  process  of  finding  square  root  will  be  understood 
to  better  advantage  if  we  first  note  the  close  relation  between  the 
process  of  squaring  a  number  and  the  area  representing  the  same 
number  of  square  units. 

Consider  the  number  36  and  the  square  whose 

side  is  36  units  m  length. 

36  30  +6 

36  30  +6 


216  30X6  +62 

108  302+    30x6 


>o 


1296  302  4-2(30  X6)  +62  =  900  +360  +36  =  1296.  ^o 


SQUARE  ROOT 


153 


It  will  be  clear  to  the  student  that : 

(1)  The  square  area  is  made  up  of  two  squares  and  two  rcc* 
tangles ;  and 

(2)  The  dimensions  of  the  two  equal  rectangles  are  the  lengths 
of  the  sides  of  the  two  squares. 

Finding  the  Square  Root  of  a  Given  Number. 

Illustration : 

Find  the  square  root  of  1296. 

Separate  the  number  into  periods  of 
two  figures  each. 

12  96130+6 

30 


30 


=     900 


302 

60  I   3  96 

(60  +  6)6=1   3  96 


30 


30 


The  greatest  square  contained  in  the 
Hundreds'  period  is  900. 

The  square  root  of  900  is  30.     Sub- 
tract 302,  or  900,  from  1296. 

Write  30  for  the  first  part  of  the  result. 
Multiply  30  by  2. 

Reference  to  the  drawing  will  explain  the  need  for  multiplying  30  by 
2.     When  the  square  "900"  is  removed,  there  remains  an  area  whose 
length  is  30  +30,  or  60.     Hence,  the  remainder  of  396  square  units  has  a 
tength  of  60.     60  is  the  Trial  Divisor.     (2  X  30.) 
Divide  396  by  60. 
This  division  of  an  area  by  the  length,  60,  gives  the  other  dimension, 
width.     Hence,  the  quotient,  6,  is  the  w4dth  of  the  remaining  area. 
Write  6  for  the  second  part  of  the  root. 
Add  6  to  the  trial  divisor,  60,  making  60+6. 

This  addition  is  necessary  because  the  length  of  the  side  of  the  small 
squares  must  be  included  in  the  length  of  the  unused  area,  396. 
Multiply  60+6,  or  66,  by  6. 

This  product  of  length,  66,  by  width,  6,  gives  area.     Or,  396, 
Subtract  this  product,  396,  from  the  remainder,  396. 
We  obtain  0,  hence,  the  exact  root  has  been  found. 
Therefore,  the  square  root  of  1296  is  36.     Result. 


154 


ROOTS 


It  will  be  found  that  division  by  the  trial  divisor  is  frequently 
an  approximate  division,  for  we  cannot  always  find  the  exact 
quotient   as  in  the  simple   case  illustrated. 

1.   Find  the  square  root  of  18769. 

Beginning  at  the  right,  separate  the  num- 
ber into  periods  of  two  places  each. 

The  greatest  square  contained  in  the  first 
period  is  1.     Subtract  1. 

The  next  period  is  87. 

The  trial  cUvisor  is  20.     ^2  X 10.) 

87  will  contain  20  at  least  4  times,  but  we 
must  allow  for  the  part  of  the  root  that  must  be  added.     Hence,    the 
approximate  quotient  is  3.     Add  3,  and  multiply  by  3. 

The  next  period  is  1860. 

The  trial  divisor  is  260.      (2X130.) 

1869  contains  260  at  least  7  times. 

Add  7  and  multiply  by  7, 

The  remainder  is  0,  and  the  exact  root  has  been  found. 


1  87  69  137 

12          =1 

20 

87 

(20+3)  X3  = 

69 

260 

1869 

(260+7)  X7  = 

1869 

22 

40 
(40+4)  X 4      = 

4800 
(4800+5)  X5  = 


5  78  40  2512405 
4 

178 
176 


2.    Find  the  square  root  of  5784025. 

In  this  example  the  process  is  similar 
to  that  already  illustrated  except  in 
one  detail.  The  second  remainder  is 
2,  and  on  annexing  the  next  period,  40, 
we  find  that  the  entire  remainder,  240, 
will  not  contain  the  divisor,  480. 

We  write  0,  in  the  root,  annex  the 
next  period,  and  the  new  trial  divisor  is  4800.     The  remainder,  24025, 
contains  4800  at  least  5  times.     Add  5  to  the  root  and  to  the  trial  divisor 
and  proceed  as  in  the  other  illustrations. 


2  40  25 
2  40  25 


BLACKBOARD   PRACTICE 


Find  the  square  root  of 
1.  1156.    6.  1764. 


2.  1225. 

3.  1849. 

4.  1521. 
6.  1936. 


7.  2025. 

8.  2601. 

9.  2916. 
10.  1681. 


11.  3136. 

12.  3481. 

13.  3249. 

14.  4356. 

15.  4096. 


16.  4761. 

17.  5476. 

18.  5184. 

19.  6241. 

20.  7744. 


21.  7396. 

22.  8649. 

23.  9409. 

24.  9216. 

25.  9604. 


SQUARE  ROOTS 


155 


26.  14641. 

27.  18225. 

28.  16129. 

29.  15376. 

30.  19044. 

31.  22801. 

32.  21609. 

33.  24964. 


34.  30625. 

35.  29584. 

36.  32761. 

37.  38416. 

38.  41209. 

39.  43264. 

40.  91204. 

41.  93025. 


42.  95481. 

43.  103041. 

44.  124609. 

45.  150544. 

46.  236196. 

47.  332929. 

48.  418609. 

49.  597529. 


50.  788544. 

51.  808201. 

52.  958441. 

53.  27144100. 

54.  35640900. 

55.  26224641. 

56.  64080025. 

57.  81270225. 


.012  = 


.0001. 


.00P=  .000001. 


.OOOP  =  .00000001. 


Finding  the  Square  Root  of  a  Decimal. 

We  have  found  that  the  number  of  figures  in  the  square  root  of 
a  number  depends  upon  the  number  of  figures  in  the  given  square. 
A  definite  relation  exists  also  between  the  number  of  figures  in  a 
decimal  square  and  its  square  root. 

.12=  .01.     One  decimal  figure  in  the  decimal;  two  in  the 

square. 
Two  decimal  figures  in  the  decimal :  four  in  the 

square. 
Three  decimal  figures  in  the  decimal :  six  in  the 

square. 
Four    decimal   figures   in    the   decimal :  eight   in 

the  square. 

In  general,  therefore,  there  are  twice  as  many  figures  in  a 
decimal  square  as  there  are  figures  in  its  square  root. 

To  point  off,  or  separate  a  decimal  square  into  periods  : 
Begin  at  the  decimal  point  and  point  off  two  figures  to  the  right 
for  each  period. 

From  this  principle  combined  with  the  principle  that  governs 
with  whole  numbers  we  may  point  off  numbers  that  are  part 
integral  and  part  decimal. 

Thus  :       14197824     is  separated  14  19   78  24  sq.  rt.  =  3768. 

is  separated  14  19  .  78  24  sq.  rt.  =  37.68. 

is  separated  14  19  78  .  24  sq.  rt.  =  376.8. 

is  separated  .14  19  78  24  sq.  rt.  =  .3768. 


14197824 
1419.7824 
141978.24 
.14197824 


156 


ROOTS 


Instead  of  separating  the  periods  by  spaces  many  mathemati- 
cians prefer  to  use  a  small  accent  placed  over  the  last  figure  of 
each  period. 


Thus: 


0  r  ^  ^ 


14197824  may  be  separated  14197824. 
1419.7824  may  be  separated  1419.7824. 


In  finding  the  square  root  of  a  number  wholly  or  partially 
decimal,  we  point  off  as  indicated  and  extract  the  square  root 
just  as  if  it  were  a  whole  number. 

Point  off  as  many  places  at  the  right  of  the  root  as  there  are 
decimal  periods  in  the  given  number. 

Illustration : 

Find  the  square  root  of  0.14197824. 


^      ^      ^ 


32 
60 

(60+7)  X7      = 

740 
(740+6)  X6    = 

7520 
(7520+8)  X8  = 


Hence,  .3768.     Result. 


14197824 

1.3768 

9 

The    root    figures    obtained    are 

r 

.19 

3768. 

4 

t69 

Counting  from  the   right   of   the 

5078 

square  we  have  four  periods  in  the 

4476 

decimal. 

60224 

Therefore,  for  the  decimal  point 

60224 

in  the  root  count  four  places  from 

the  right. 

Find  the  square  root  of  54.804409. 


p         m         r 


54.804409 17  403 
49 


140 
(140+4)  X4      = 

14800 
(14800 +3)  X3  = 


5  80 
5  76 


44409 
44409 


There  are  three  periods  in  the 
decimal. 

For  the  decimal  point  in  the  root 
point  off  three  places  from  the  right. 

Hence,  7.403.     Result. 


SQUARE  ROOT 


157 


Finding  the  approximate  square  root  of  a  number  which  is  not 
a  perfect  square. 

When  a  number  is  not  a  perfect  square  we  may  annex  zeros  and 
carry  out  the  root  to  as  many  decimal  places  as  desired. 

Ilkistration : 

Find  the  square  root  of  f  to  three  decimal  places. 

Changing  |  to  a  decimal,  |  =  .75. 

Since  three  decimal  places  are  required  in  the  result,  and  since  two 
decimal  places  in  the  square  give  one  decimal  place  in  the  root,  we  must 
find  the  square  root  of  .750000.  That  is,  six  decimal  places  must  be  used 
to  obtain  a  root  which  will  have  three  places. 

.866+ 

Therefore,  the  square  root   of  |  =» 


82 

160 
(160+6)  X6   = 

1720 
(1720+6)  X6  = 


.750000 
64 


1100 
996 


10400 
10356 


44 


.866. 

When  a  root  is  not  exact  it  is  cus- 
tomary to  obtain  the  number  of 
decimal  places  asked  for,  and  to  indi- 
cate the  approximate  nature  of  the 
root  by  affixing  the  sign  "  +." 


BLACKBOARD   PRACTICE 

Find  the  square  root  of : 


1. 
2. 
3. 
4. 


26.4196. 
2641.96. 
.264196. 
2992.09. 


5. 
6. 
7. 
8. 


.355216. 
.001296. 
.000729. 
3003.04. 


9.  .00717409. 

10.  .00032761. 

11.  4943.4961. 

12.  96.177249. 


13.  .00013689. 

14.  .00003249. 

15.  250300.09. 

16.  6403.2004. 


Find,  to  three  decimal  places,  the  square  root  of : 

17.  150.  21.    1200.  25.    124356.  29. 

18.  325.      22.  17500.    26.  208070.     30. 

19.  570.      23.  35410.    27.  154.118.    31. 

20.  791.      24.  65117.    28.  3456.77.    32. 

Find  the  square  root  of  the  following  to  three  decimal  places. 

33.  f.  35.    f.  37.    ii- 

34.  f.  36.    |.  38.    if. 


.18763. 
.000177. 
.511411. 
675.4030. 


40      4  10 


158  ROOTS 

WRITTEN   APPLICATIONS   OF   SQUARE  ROOT 

1.  How  many  feet  are  there  in  the  side  of  a  square  whose  area 
is  4624  square  feet  ? 

2.  The  total  area  of  the  six  faces  or  sides  of  a  cube  is  3456  square 
inches.     What  is  the  length  of  each  edge  of  the  cube? 

3.  How  many  feet  in  the  side  of  a  square  field  containing  1  acre, 
if  an  acre  is  equal  to  43,560  square  feet  ? 

4.  A  farmer  built  a  fence  around  a  square  field  known  to  con- 
tain 640  square  rods.     How  many  feet  in  the  length  of  the  fence? 

5.  A  contractor  uses  14,400  paving  tiles,  each  6  inches  square, 
for  covering  a  square  courtyard.  What  is  the  length  of  the  sides 
of  the  yard  in  feet  ? 

6.  A  man  walking  at  the  rate  of  4  miles  per  hour  goes  around 
a  square  park  whose  area  is  160  acres.  In  how  many  hours  can 
he  go  once  around  the  park? 

7.  A  fence  is  built  around  a  square  court  known  to  contain 
15625  square  feet.     At  $1.25  per  foot,  find  the  cost  of  the  fence. 

8.  Jack  and  his  father  walked  around  a  square  field  whose 
area  was  exactly  22^  acres.  How  many  rods  did  they  walk  in  go- 
ing around  it  ? 

9.  A  lot  160  ft.  deep  and  90  ft.  wide  on  a  street  sold  for  $40 
a  front  foot.  How  much  should  be  received  for  a  square  lot  of 
the  same  area  at  the  same  price  per  front  foot  ? 

10.  A  real  estate  agent  gave  a  building  lot  150  fpet  long  and 
100  feet  wide  in  exchange  for  a  square  corner  lot  containing  the 
same  amount  of  ground.  Find  the  length  of  the  sides  of  the  square 
lot. 

11.  In  attempting  to  arrange  1000  boys  in  a  square  formation 
at  an  exhibition,  a  gymnasium  instructor  finds  that  he  has  39  boys 
who  are  not  included  in  his  square.  How  many  boys  are  there 
on  each  side  of  the  square? 


THE   RIGHT   TRIANGLE 


A  Right  Triangle  is  a  triangle  that  contains  a  right  angle. 

In  the  figure, 

A-SC  is  a  right  triangle. 

The  angle  at  B  is  a  right  angle. 

The  Hypotenuse  of  a  Right  Triangle  is  the 
side  opposite  the  right  angle. 

b 

AC  is  the  hypotenuse  of  the  right  triangle  ABC. 

The  Legs  of  a  Right  Triangle  are  the  two  sides  that  include  thf 
right  angle. 

BA  and  BC  are  the  legs  of  the  right  triangle  ABC. 

For  convenience  we  frequently  refer  to  the  side  BA  as  the  base 
of  the  triangle,  and  to  the  side  BC  as  the  altitude,  but  these  terms 
apply  only  in  particular  cases. 

By  geometry  it  may  be  proved  that 

In  any  right  triangle  the  square  drawn 
upon  the  hypotenuse  is  equal  to  the  sum  of 
the  squares  drawn  upon  the  legs. 

That  is,  in  the  figure, 

c  is  the  hypotenuse,  a  and  h  are  the  legs. 

Then :  The  area  of  the  square  whose  side 
is  c  is  equal  to  the  area  of  the  square  on  b  plus 
the  area  of  the  square  on  a.     Or, 

In  many  right  triangles  this  relation  can 
be  seen  at  once  by  dividing  the  three  squares 
into  unit  squares. 

Thus,  in  the  figure,  the  length  of  the  hy- 
potenuse is  5,  and  the  lengths  of  the  legs,  4 
and  3  respectively.     That  is, 


^  *         ■  bA-  ■    .1 


52=42+32. 

25  =  16+9. 


159 


160 


THE  RIGHT  TRIANGLE 


To  find  the  length  of  the  hypotenuse  of  a  right  triangle : 
Since,  in  any  right  triangle, 

Extracting  the  square  root  of  both  expressions, 

Or,  The  length  of  the  hypotenuse  of  a  right  triangle  equals  the 
square  root  of  the  sum  of  the  squares  on  the  legs. 

Illustration : 

1.  Find  the  length  of  the  hypotenuse  of  a 

right  triangle  whose  legs  are  6  feet  and  8  feet 

respectively. 

The  figure  will  aid  in  the  solution,  and  we  will 
let  the  hypotenuse  be  represented  by  h. 
Then:  h^=6^-\-8\ 

Whence, 

h  =  V62+82  =  V36+64  =  VlOO"=  10.     Result. 

2.  Find  the  length  of  the  hypotenuse  of  the 
right  triangle  in  the  figure. 

h  =  V122+152  =  V144+225  =  Vsm  =  19.2094. 

Result. 

BLACKBOARD   PRACTICE 

Draw  a  right  triangle  to  represent  each  of  the  following  cases, 
and  find  the  length  of  the  hypotenuse  if  the  length  of  the  legs  are, 
respectively, 

1.  12  in.,  and  16  in.  8. 

2.  15  in.,  and  20  in.  9. 

3.  18  ft.,  and  24  ft.  10. 

4.  24  ft.,  and  32  ft.  11. 

5.  48  ft.,  and  64  ft.  12. 

6.  5  ft.,  and  12  ft. 

7.  10  rd.,  and  24  rd. 


12  ft.,  and  14  ft. 
15  ft.,  and  30  ft. 
25  ft.,  and  30  ft. 
50  ft.,  and  75  ft. 
75  ft.,  and  80  ft. 

13.  90  ft.,  and  100  ft. 

14.  110  ft.,  and  140  ft. 


THE  DIAGONAL  OF  A  SQUARE 


161 


To  Find  the  Length  of  the  Diagonal  of  a  Square  or  Rectangle. 
The  Vertices  of  a  square  or  a  rectangle  are  the  meeting  points 
of  the  sides. 

In  the  figure  the  vertices  are  A,  B,  C,  and  D. 

The  Diagonals  of  a  square  or  a  rectangle 
are  the  two  straight  lines  joining  opposite 
vertices. 

In  the  figure  the  diagonals  are  AC  and  BD. 

As  the  angles  of  a  square  or  rectangle  are 
right  angles  we  may  form  a  right  triangle  in 
either  by  drawing  one  diagonal.     Therefore, 

The  diagonal  of  a  square  is  the  hypotenuse  of  a  right  triangle  having 
equal  legs,  and  the  diagonal  of  the  rectangle  A  BCD  is  the  hypotenuse 
of  a  right  triangle  having  unequal  legs. 

Illustrations : 

1.  Find  the  length  of  the  diagonal  of  the  floor  of  a  square  room, 

the  length  of  whose  side  is  24  feet.  - 

The  figure  represents  the  floor  of  the  room,  and 
we  are  to  find  the  hypotenuse  of  a  right  triangle 
whose  legs  are  each  24  feet  long. 

/i2  =  242+242  =  576 +576  =  1152. 
Then  /i  =  Vl  152  =33.94.     Or,  33.94  + feet. 

Result. 

2.  A  man  stands  at  the  corner  of  a  field  350  feet  long  and  250 

feet  wide.     If  he  goes  diagonally  across  the  field  to  the  corner 

opposite,  how  much  less  distance  does 

he  travel  than  by  going  along  two  sides  ? 

The  figure  represents  the  field,  and  the 
man  starts  at  A.     Find  the  length  of  AC. 

AC  =  V3502+2502 

=  Vl22500 +62500 

=  Vl85000 

=  430. 11  + feet. 
The  distance  around  two  sides  =350+250  =600  feet. 
Hence,  he  saves  (600-430.11+)  feet  =  169.89-feet. 


162  THE  RIGHT  TRIANGLE 

BLACKBOARD   PRACTICE 

Find  the  diagonal  of  a  square  whose  side  is : 

1.  10  feet.  3.   30  feet.  5.   40  rods.  7.   90  yards. 

2.  15  feet.  4.    50  feet.  6.    65  rods.  8.    100  yards. 

Find  the  diagonal  of  a  rectangle  whose  length  and  width  re- 
spectively are : 

9.    15  feet,  10  feet.  12.   40  yards,  15  yards. 

10.  20  feet,  12  feet.  13.    50  rods,  30  rods. 

11.  30  yards,  12  yards.  14.    100  rods,  65  rods. 

To  find  the  length  of  one  leg  of  a  right  triangle  when  the  length 
of  the  hypotenuse  and  the  length  of  the  other  leg  are  given. 

We  have  learned  that  the  square  drawn  upon  the  hypotenuse 
of  a  right  triangle  is  equal  to  the  sum  of  the  squares  drawn  upon 
its  legs. 

That  is,  c'  =  a''+h^ 

Writing  this  expression  in  the  form  a'^-{-¥  =  c^,  and  subtracting 
6^  from  both  members,  we  have :      Or,  subtracting  a^  from  both 

members, 

6^  =  b^  a^        =  a^ 

That  is,     a2  =  c^ -hK  That  is,     ¥  =  c^ -a\ 

And,  a=Vc^-b\  And,  h  =  Vc^-a\ 

Either  leg  of  a  right  triangle  is  equal  to  the  square  root  of  the  dif- 
ference of  the  square  on  the  hypotenuse  and  the  square  on  the  other  leg. 

BLACKBOARD    PRACTICE 

Find  the  length  of  one  leg  of  a  right  triangle  when  the  length 
of  the  hypotenuse  and  the  length  of  the  other  leg  are,  respectively : 

1.  12  feet,  9  feet.    4.    15  yards,  10  yards.  7.   75  feet,  60  feet. 

2.  20  feet,  15  feet.  5.    24  rods,  20  rods.       8.    90  feet,  80  feet. 

3.  45  feet,  30  feet.  6.   45  yards,  36  yards.  9.    100  rods,  60  rods. 


APPLICATIONS 


163 


WRITTEN   APPLICATIONS    OF    THE   RIGHT    TRIANGLE 

1.  One  of  the  most  common  sizes  in  manufactured  rugs  is  the 
"  9  by  12,"  which  is  9  feet  wide  and  12  feet  long.  What  is  the 
length  of  its  diagonal?  What  is  the  length  of  the  diagonal  of  a 
''6  by  9"  rug? 

2.  Measure  the  length  and  the  width  of  the  floor  of  any  rectan- 
gular room,  and  calculate  the  length  of  the  diagonal  in  feet  and 
inches,  to  the  nearest  inch.  Then  measure  the  diagonal  carefully, 
and  compare  the  measurement  with  your  calculation. 

3.  A  father  and  son  during  their  daily 
walk  came  to  a  corner  of  a  field  at  A.  The 
father  walked  around  the  field,  going  90  rods 
along  AB,  and  67.5  rods  along  BC ;  but  the 
boy  went  straight  across  the  field  from  A  to  C. 
Find  the  number  of  rods  that  each  walked. 

4.  A  small  park  at  the  intersection  of 
three  streets  is  shaped  like  a  right  triangle, 
and  the  sides  which  include  the  right 
angle  are  160  feet  and  120  feet  respec- 
tively. Find  the  cost  of  inclosing  the  plot 
with  a  concrete  curb  costing  $1.10  a  run- 
ning foot. 
At  a  point  on  a  river  bank  180  feet  from  the  opposite  bank 

a  swimmer  starts  to  swim  straight  across,  but  the  current  carries 

» 

him  downstream  so  that  he  lands  at  a  point  80  feet  down  the 
river  and  on  a  line  at  right  angles  to  his  intended  line  of  crossing. 
How  far  does  he  actually  swim? 

6.  A  room  is  24  feet  long,  18  feet 
wide,  and  10  feet  high  from  the  floor  to 
the  ceiling.  What  is  the  distance  in  feet 
and  inches  from  any  one  of  the  lower 
corners  of  the  room  to  the  opposite  upper 
corner  ? 


-J   L 


_/  ^ 


5. 


164 


THE  RIGHT  TRIANGLE 


7.  A  window  sill  in  a  house  is  16  feet 
from  the  ground,  which  is  level,  and  a  ladder 
20  feet  long  is  so  placed  that  the  upper  end 
of  it  rests  upon  the  sill.  How  far  is  it  from 
the  foot  of  the  ladder  to  the  point  in  the  wall 
directly  under  the  window? 


8.  Jones  and  Brown  start  at  the  same  time  and  at  the  same 
point,  Jones  going  straight  east  for  7  hours,  while  Brown  goes 
straight  south  for  7  hours.  If  Jones  travels  20  miles  an  hour, 
and  Brown  travels  28  miles  an  hour,  how  many  miles  apart  will 
they  be  at  the  end  of  seven  hours  ? 

9.  The  height  of  a  roof  at  the  peak 
is  6  feet  above  the  height  at  the  eaves, 
and  the  width  of  the  building  is  30  feet. 
Allowing  1  foot  for  the  "  overhang," 
how  long  must  a  carpenter  cut  the 
*'  rafter  '^  AJ5  in  the  figure? 


10.  A  stairway  is  made  up  of 
12  steps,  each  ^'  tread  "  being  12 
inches  wide,  and  each  "  riser  "  9 
inches  high.  Calculate  the  length 
of  the  ^'  stringer  "  necessary  for  the 
stairs. 


11.  A  pole  is  supported  on  two  opposite  sides  by  wires,  one  of 
which  stretches  from  the  top  of  the  pole  to  the  ground  level  with 
the  pole,  while  the  other  stretches  from  the  top  of  the  pole  to  the 
top  of  a  wall  20  feet  high.  If  the  pole  is  65  feet  high,  the  long 
wire  90  feet  in  length,  and  the  short  wire  60  feet  in  length,  find  the 
distance  from  the  foot  of  the  wall  to  the  foot  of  the  long  wire. 
(Draw  a  figure  to  illustrate  the  problem.) 


THE   CIRCLE 

A  Circle  is  a  figure  bounded  by  a  curved  line,  all  points  of  which 
are  equally  distant  from  a  point  within  called  the  Center 


po^f^e/v. 


Because  of  the  needs  of  later  mathematics,  the  circle  may  he 
defined  as  a  curved  line,  all  points  of  which  are  equally  distant 
from  a  point  within  called  the  center. 

The  Circumference  is  the  length  of  the  bounding  line  of  a  circle. 

The  Radius  is  the  distance  from  the  center  to  any  point  on 
the  circumference.     (The  plural  of  radius  is  radii.) 

The  Diameter  of  a  circle  is  the  distance  from  any  point  on  the 
circumference  measured  through  the  center  and  ending  in  the 
circumference. 

The  circumference,  radius,  and  diameter  are  indicated  in  the 
illustrations  above. 

THE   LENGTH   OF   THE   CIRCUMFERENCE   OF   A   CIRCLE 

The  length  of  the  circumference  of  a  circle 
has  been  found  to  be  very  nearly  3.1416 
times  the  length  of  the  diameter.  That  is, 
in  the  figure,  the  distance  from  A  around 
the  circumference  to  A  is  nearly  3.1416 
times  the  distance  from  A  through  the 
center  to  B. 

Since  the  decimal  .1416  is  a  little  too  large,  we  express  the  re- 
lation of  circumference  to  diameter  more  accurately  if  we  say 
that  the  circumference  is  approximately  3.1416—  times  the  di- 
ameter. 

165 


166  THE  CIRCLE 

In  the  case  of  small  circles  we  may  use  S},  or  ^^-,  instead  of 
3.1416-,  and  our  results  will  be  reasonably  accurate. 

In  the  following  exercise  the  pupil  should  draw  in  each  case  a  circle  to 
represent  the  problem,  placing  upon  this  circle  the  given  lines.  After 
finding  the  required  result,  write  it  upon  the  line  whose  length  is  sought. 

BLACKBOARD   PRACTICE 

4 

Using  3. 14 16-,  find,  approximately,  the  circumference  of  a 
circle  whose  diameter  is  : 

1.  15  in.  6.  2.7  in.  11.  21.4  ft.  16.  5.12  yd. 

2.  20  in.  7.  3.7  ft.  12.  13.5  yd.  17.  3.08  rd. 

3.  42  in.  8.  5.8  ft.  13.  20.5  yd.  18.  1.75  yd. 

4.  34  ft.  9.  9.2  yd.  14.  31.4  rd.  19.  50.9  rd. 

5.  27  rd.  10.  8.5  rd.  15.  5.25  rd.  20.  150.5  yd. 

Using  3.1416-,  find,  approximately,  the  circumference  of  a  circle 
whose  radius  is : 

21.  5  ft.  25.  3  ft.  6  in.  29.  15.75  yd. 

22.  7.5  ft.  26.  4  ft.  10  in.  30.  125.75  yd. 

23.  9.25  ft.  27.  3  yd.  2  ft.  31.  131.05  rd. 

24.  10.5  ft.  28.  5  rd.  3  yd.  32.  250.5  ft. 

Using  3|,  find,  approximately,  the  circumference  of  a  circle 
whose  diameter  is : 

33.  14  in.  36.   42.5  in.  39.    142  ft.  42.    .434  ft. 

34.  28  in.  37.    25.1  ft.  40.    253  yd.         43.    1.04  yd. 

35.  35  in.  38.    37.8  yd.        41.    45.5  yd.        44.    11.42  rd. 

To  fimd  the  diameter  of  a  circle  when  the  circumference  is  given, 
divide  the  given  circumference  by  3.1416.  (The  result  will  be 
slightly  larger  than  the  true  diameter.) 

THE   AREA   OF   A   CIRCLE 

If  we  think  of  a  circle  as  composed  of  a  very  large  number  of 
little  triangles,  we  can  imagine  these  triangles  laid  out  in  a  straight 
line  as  in  the  figure. 


AREA  OF  A  CIRCLE 


167 


Tn  the  figure 

AC  is  the  length  of  the  circum- 
ference. 
Also 

AC  is  the  sum  of  the  bases  of  all 
the  triangles. 

Now  each  little  triangle  has  an  altitude  approximately  equal 
tu  the  radius  of  the  circle,  and  if  the  triangles  were  small  enough 
Ro  as  to  be  exact  triangles,  their  total  area  would  be 


Or, 


^  altitude  X  sum  of  all  the  bases, 

i  radius  X  circumference  of  the  circle. 


That  ib, 

The  Area  of  the  Circle  =  4-  product  of  radius  X  circumference. 
But    the    circumference  =  3. 1416-  X diameter,    or,     3.1416-  X 
(twice  the  radius). 
Or,  using  lettsrs,  Area  =  4-  RXS.UIQ-  X2  R 

7?X3.1416-  X2XR 


^,    ,  .  =3.1416-  XR^. 

That  IS, 

The  area  of  n  circle  equals  3. 141 6-  times  the  square  of  the 

radius. 

Illustrations ! 

Find  the  area  of  a  circle  whose  radius  is  12  inches. 

Squaring  the  radius,  12-  =  144. 

Then,  Area  =  3.1416- X 144  square  inches 

=  452.3904  square  inches.     Result. 


168  THE  CIRCLE 

Find  the  area  of  a  circle  whose  diameter  is  17  feet. 

The  radius  17^2  =8.5  feet. 

Squaring  the  radius,  S.S^  =  72.25  square  feet. 

Then,  Area  =3.1416-  X72.25  square  feet. 

BLACKBOARD   PRACTICE 

Using  3|,  find  approximately  the  area  of  a  circle  whose  radius  is : 


1. 

7  in. 

6.    7.7  in. 

11.    .14  ft. 

16. 

2.5  ft. 

2. 

10  in. 

7.    5.6  in. 

12.   2.8  ft. 

17. 

5.3  ft. 

3. 

14  in. 

8.   4.3  in. 

13.    9.1ft. 

18. 

6.1  ft. 

4. 

21  in. 

9.    128  in. 

14.    14.7  in. 

19. 

8.2  ft. 

5. 

30  in. 

10.    149  in. 

15.    210  in. 

20. 

9.8  ft. 

Usi: 

Qg  3.1416- 

- ,  find  the  area  of 

a  circle 

Wh 

ose  radius 

is: 

Whose  diameter  is : 

21. 

12  in. 

25.   31  ft. 

29.    12  in. 

33. 

7.8  ft. 

22. 

16  in. 

26.   4.2  ft. 

30.    18  in. 

34. 

5.7  ft. 

23. 

28  in. 

27.    5.1  ft. 

31.    14  ft. 

35. 

61yd. 

24. 

32  in. 

28.    7.3  ft. 

32.    19  ft. 

36. 

8.4  yd. 

37.  What  is  the  area  of  the  end  of  a  circular  stone  column 
whose  diameter  is  15  inches? 

38.  What  is  the  area  of  the  bottom  of  a  circular  tin  pail  whose 
diameter  is  10  inches? 

39.  What  is  the  area  of  the  bottom  of  a  circular  catch-basin 
whose  diameter  is  4.2  feet? 

40.  A  circular  pond  whose  diameter  is  45  feet  has  a  concrete 
bottom.  What  is  the  area  of  the  concrete  surface  in  the  bottom 
of  the  pond  ? 

41.  The  piston-head  in  the  cylinder  of  a  locomotive  is  20  inches 
in  diameter.  How  many  square  feet  are  there  in  the  area  of  this 
piston-head  ? 

42.  A  concrete  paving  at  the  base  of  a 
fountain  is  shaped  as  in  the  figure.  Find  the 
number  of  square  feet  in  its  area. 


APPLICATIONS 


169 


60' 


WRITTEN   APPLICATIONS 

Problems  Involving  Combinations  of  the  Rectangle,  the  Tri- 
angle, and  the  Circle  in  a  Single  Area. 

1.  What  is  the  area  of  a  plot  of  ground 
shaped  as  in  the  figure?  What  is  the  value 
of  the  plot  at  S240  an  acre?  (1  A.  =43,560 
sq.  ft.) 


50  rd 


o 


2.  A  city  building  lot  is  shaped  as 
in  the  figure.  At  the  rate  of  $4000 
an  acre,  what  is  the  value  of  the 
lot? 


40  rd 


3.  Four  city  streets  intersect 
as  in  the  figure,  and  the  inclosed 
plot,  which  is  400  feet  long  and 
300  feet  wide,  was  sold  at  the  rate 
of  $16,000  an  acre.  How  much 
did  the  plot  sell  for? 


y  jL 


1  r 


/ 


C5 


300' 


along 


A  builder  lays  a  concrete  walk 
two  sides  of  a  new  corner 
property.  At  $1.40  a  square  yard, 
find  the  cost  of  the  walk,  if  it  is  6  feet 
wide. 


5.  A  school  athletic  association 
constructed  a  cinder  track  shaped 
as  in  the  figure,  at  a  cost  of  $.80 
a  square  yard.  If  the  width  of  the 
track  was  12  feet,  the  straightaway 
length  was  500  feet,  and  the  radii  of  the  ends  50  feet,  find  the 
cost  of  the  track. 


170 


THE  CYLINDER 


THE    CYLINDER 


If  a  rectangle  is  revolved  about  one  of  its  sides  as  an  axis, 
the  solid  formed  is  called  a  Cylinder. 

If  AB,  in  the  figure  at  the  left,  remains  fixed  and  the  rectangle 
BCD  A  revolves  about  AB,  the  rectangle  in  its  revolution  forms 
a  cyUnder. 

The  two  circles  that  are  formed  by  AD  and  BC  are  called  the 
Bases  of  the  Cylinder. 

The  distance  between  the  bases  is  called  the  Altitude  of  the 
Cylinder. 

The  curved  surface  made  by  the  line  CD  is  called  the  Lateral 
Surface. 


THE  VOLUME   OF  A   CYLINDER 

We  have  found  that  the  volume  of  a  rectangular  solid  equals 
the  product  of  the  number  representing  the  square  units  in  the 
area  of  its  base  by  the  number  representing  the  units  in  its  height. 

In  like  manner,  therefore  : 

The  volume  of  a  cylinder  equals  the  product  of  the  number 
representing  the  square  units  in  the  area  of  the  base  by  the  num- 
ber representing  the  units  in  the  height.     Or,  briefly, 

Volume  of  a  cylinder  =  The  number  of  units  in  the  area  of  the 
base  times  the  number  of  units  in  the  altitude. 


VOLUME  OF  A  CYLINDER  171 

Illustrations : 

1.  Find  the  volume  of  a  cylinder  the  area  of  whose  base  is  6 
square  inches,  and  whose  altitude  is  10  inches. 

Volume  =  area  of  base  times  altitude 
=  (6  X 10)  cubic  inches. 
=  60  cubic  inches.     Result. 

2.  Find  the  volume  of  a  cylinder  whose  base  is  10  inches  in 
diameter,  and  whose  altitude  is  20  inches. 

Using  the  rule  for  finding  the  area  of  the  circular  base, 
Radius  of  base  =5  in. 

Area  of  base  =3.1416  XS^  =  3.1416  X25  =  78.54  sq.  in. 
Volume  =  area  of  base  times  altitude 

=  (78.54X20)  cu.  in. 

=  157.08  cu.  in.     Result. 

BLACKBOARD    PRACTICE 

Find  the  volume  of  a  cylinder  whose  altitude  and  base  area 
respectively  are : 

1.  10  in.,  8  sq.  in.  8.  2  ft.  6  in.,  15  sq.  in. 

2.  12  in.,  10  sq.  in.  9.  3  ft.  4  in.,  4.2  sq.  in. 

3.  12  in.,  12  sq.  in.  10.  5  ft.  9  in.,  6.75  sq.  in. 

4.  16  in.,  8  sq.  in.  11.  8  ft.  4  in.,  4  sq.  ft. 

5.  24  in.,  30  sq.  in.  12.  9  ft.  6  in.,  5  sq.  ft.  24  sq.  in. 

6.  48  in.,  35  sq.  in.  13.  10  ft.  8  in.,  6  sq.  ft.  72  sq.  in. 

7.  66  in.,  24  sq.  in.  14.  14  ft.  10  in.,  7  sq.  ft.  96  sq.  in. 

Find  the  volume  of  a  cylinder  whose  altitude  and  the  radius 
of  whose  base  respectively  are  : 

15.  14  in.,  5  in.  21.  3  ft.  6  in.,  1  ft.  4  in. 

16.  16  in.,  9  in.  22.  4  ft.  3  in.,  2  ft.  3  in. 

17.  24  in.,  4  in.  23.  6  ft.  4  in.,  2  ft.  8  in. 

18.  12  ft.,  2  ft.  24.  7  ft.  6  in.,  3  ft.  1  in. 

19.  20  ft.,  3  ft.  25.  8  ft.  4  in.,  4  ft.  6  in. 

20.  22  ft.,  3  ft.  26.  10  ft.  6  in.,  5  ft.  9  in. 


172  .  THE  CYLINDER 

Capacity  of  Silos.  The  capacity  of  a  silo  may  be  estimated  in 
tons  or  in  cubic  feet.  The  silo  is  used  for  storing  silage  to  be  used 
in  the  winter.  While  the  practice  varies  under  different  conditions 
and  in  different  places,  for  our  discussion  we  will  assume  that 

1  cubic  foot  of  silage  weighs  40  pounds. 
Then,       50  cubic  feet  of  silage  =  1  ton. 

The  amount  of  silage  fed  daily  to  a  cow  varies  in  different 
sections,  but  for  this  book  it  is  assumed  that  a  recognized  average 
daily  feeding  is  1^  cubic  feet  of  silage.  As  the  feeding  season  is 
about  six  months,  a  cow  will  eat  in  that  time 

6X30X1^  =  270,  the  number  of  cubic  feet  of  silage. 

Or,  allowing  for  waste,  300  cubic  feet  of  silage  per  cow  per  year. 
Silos  are  usually  built  cylindrical  in  shape,  and  are  generally 
constructed  of  wood,  brick,  tile,  or  concrete. 
Illustrations : 

1.  How  many  tons  of  silage  can  be  placed  in  a  cylindrical  silo 
10'  in  diameter  and  18'  high? 

Area  of  the  base  =3.1416X52  =78.54  sq.  ft. 

Volume  of  cyUnder  =  78.54  X 18  =  1413.72  cu.  ft. 

Since  1  ton  =50  cu.  ft.  of  silage,  1413.72^50  =28.274  tons.     Result. 

2.  Allowing  1.5  cu.  ft.  of  silage  per  cow  per  day,  how  many 
days'  feed  for  30  cows  can  be  stored  in  a  silo  12  ft.  in  diameter  and 
25  ft.  high? 

Capacity  of  silo  =3.1416  X62  X  25  =2827.44  cu.  ft.  • 
Daily  consumption  =  30  X 1 .5  =  45  cu.  f t. 
Then,  2827.44-^45  =62.8  days.     Result. 

BLACKBOARD   PRACTICE 

Find  the  number  of  cubic  feet  capacity  of  a  cylindrical  silo : 

1.  10'  in  diameter,  20'  high.       4.    12'  in  diameter,  30'  high. 

2.  10'  in  diameter,  24'  high.       5.    15'  in  diameter,  24'  high. 

3.  12'  in  diameter,  24'  high.       6.    16'  in  diameter,  30'  high. 


TANKS  AND  CISTERNS  173 

Allowing  300  cu.  ft.  of  silage  per  cow  for  a  season,  how  many 
tons  will  be  required  tg  provide  feed  for : 

7.  12  cows?         9.   20  cows?       11.    35  cows?       13.    50  cows? 

8.  15  cows?       10.    25  cows?       12.   45  cows?       14.    65  cows? 

Allowing  14-  cubic  feet  of  silage  per  cow  per  day,  for  how  many 
days  will  a  silo  : 

15.  11  ft.  in  diameter  with  silage  21  ft.  high  provide  feed  for 
8  cows? 

16.  12  ft.  in  diameter  with  silage  20  ft.  high  provide  feed  for 
10  cows? 

17.  15  ft.  in  diameter  with  silage  21  ft.  high  provide  feed  for 
16  cows? 

18.  15  ft.  in  diameter  with  silage  25  ft.  high  provide  feed  for 
20  cow^s? 

19.  16  ft.  in  diameter  with  silage  27  ft.  high  provide  feed  for 
28  cows? 

20.  A  farmer  keeps  36  cows  and  requires  storage  for  enough 
silage  to  feed  1|-  cu.  ft.  daily  to  each  cow  from  November  1  to 
April  15.  How  many  tons  of  silage  must  he  provide  to  supply 
this  feed? 

Capacity  of  Tanks  and  Cisterns.  In  measuring  the  capacity 
of  tanks  we  use  three  different  units  of  measure,  the  cubic  foot, 
the  gallon,  and  the  barrel.  It  is  often  convenient  to  use  in  such 
measurements  the  weight  of  a  unit  quantity  of  a  liquid. 

EQUIVALENTS 

1  cubic  foot  of  water         =     62^  pounds.  (Approx.) 

1  cubic  foot  of  any  liquid  =       7^  gallons.  (Approx.) 

1  gallon  of  water  =       8|  pounds.  (Approx.) 

1  gallon  of  water  =   231  cubic  inches.  (Exact) 

1  barrel  of  water  =       4g  cubic  feet.  (Approx.) 

1  bushel  of  small  grain  =  2150.42  cubic  inches.  (Exact) 


174 


THE  CYLINDER 


BLACKBOARD   PRACTICE 

Change  to  cubic  inches  :  Change  to  cubic  feet : 

1.  12  gal.  4.   25  bu.  7.   45  bbl.  10.    110  gal. 

2.  19  gal.  5.    32  bu.  8.    64  bbl.  11.    165  gal. 

3.  35  gal.  6.   45  bu.  9.    120  bbl.  12.   210  gal. 

Change  to  gallons  :  Change  to  pounds  : 

13.  45  cu.  ft.  16.  1155  cu.  in.  19.    15  cu.  ft.  of  water. 

14.  70  cu.  ft.  17.  1386  cu.  in.  20.    15  gal.  of  water. 

15.  91  cu.  ft.  18.  16,170  cu.  in.  21.    12  bbl.  of  water. 

Find,  in  bushels,  the  capacity  of  a  rectangular  bin : 

22.  8'X5'X4'.  24.    10'X6'X5^  26.    12'X10'X7'. 

23.  10'X5'X3'.        25.    12'X8'X6'.  27.    16'X12'X10'. 

Find,  in  gallons,  the  capacity  of  a  rectangular  tank : 

28.  6'X5'X4'.  30.    12'X8'X6'.  32.    16'X12'X7'. 

29.  10'X6'X4'.       31.    16'X6'X4'.  33.   20'X8'X11'. 

Find,  in  barrels,  the  capacity  of  a  rectangular  tank : 

34.  8'X6'X4'.  36.    12'X7'X6'.  38.    18'X12'X8'. 

35.  10'X7'X5'.        37.    14'X8'X6'.  39.   24'X16'X12'. 

Find,  in  cubic  feet,  the  capacity  of  a  box  that  will  hold : 

40.  12  bu.    42.    45  bu.    44.    72  bu.      46.    120  bu.    48.    360  bu. 

41.  28  bu.    43.    65  bu.    45.    100  bu.    47.    250  bu.    49.    525  bu. 

Find  the  weight  of  the  water  that  fills  a  tank : 

50.  8'  6''  long,  5'  3"  wide,  2'  6"  deep. 

51.  10'  4^'  long,  6'  5''  wide,  3'  T'  deep. 

52.  16'  long,  10'  6"  wide,  6'  8"  deep. 

53.  24'  6"  long,  15'  9"  wide,  5'  10"  deep. 

Find,  in  gallons,  the  capacity  of  a  cylindrical  tank : 

54.  3'  in  diameter,  6'  long.  58.    10'  in  diameter,  12'  high. 

55.  4'  in  diameter,  7'  long.  59.    12'  in  diameter,  14'  high. 

56.  5'  in  diameter,  8'  long.           60.    18'  in  diameter,  15'  high. 
67.   4'  in  diameter,  9'  long.            61.    20'  in  diameter,  16'  high. 


BUSINESS   FORMS 
I.   ACCOUNTS 

An  Account,  in  business  practice,  is  a  record  of  transactions. 

A  Daybook  is  a  book  used  for  recording  the  business  of  a  day, 
each  transaction  being  set  down  as  it  occurs. 

Example  :  A  merchant  sells  an  article  to  a  customer  who  has  the 
privilege  of  paying  for  purchases  at  the  end  of  each  month.  The  pur- 
chase is  deUvered  to  the  customer,  and  immediately  there  is  written  upon 
the  daybook  a  statement  that  goods  to  a  certain  amount  have  been  bought. 

A  Ledger  is  a  book  in  which  all  of  the  dealings  with  an  individual, 
or  all  of  the  dealings  of  a  particular  class,  are  kept  on  one  sheet. 

This  is  accomplished  by  transferring  the  different  it^ms  on  the  day- 
book to  individual  accounts,  and  this  work  is  done  daily  or  weekly  accord- 
ing to  the  amount  of  business  done.  The  process  enables  a  merchant 
to  find  at  any  given  time  a  complete  record  of  the  transactions  with  an 
individual,  and  by  using  the  ledger  the  merchant  saves  the  trouble  and 
annoyance  of  searching  through  a  mass  of  transactions  in  his  daybook. 

Debits  in  a  ledger  account  are  the  amounts  charged  against  an 
individual  or  firm. 

In  practice  the  left  side  of  a  record  is  used  for  debits. 

Credits  in  a  ledger  account  are  the  amounts  received  from  an 
individual  or  firm. 

In  practice  the  right  side  of  a  record  is  used  for  credits. 

The  Balance  in  a  ledger  account  is  the  difference  between  the 
sum  of  the  debits  and  the  sum  of  the  credits. 

Balancing  the  Books  is  a  process  of  finding  at  regular  intervals 
the  exact  condition  of  all  the  accounts  on  the  books  of  a  firm. 

In  business  practice  it  is  a  common  custom  to  send  out  each  month  a 
record  of  transactions  for  the  last  thirty  days.  Such  a  process  is  a  form 
of  balancing  an  account,  for  it  indicates  the  condition  in  which  the  account 
stands. 

175 


176 


BUSINESS  FORMS 


Abbreviations  Used  in  Keeping  Accounts 

Account       acc't.         Credit  Cr.  Paid  Pd. 

Balance        bal.  Debit  Dr.  Payment     Pay't. 

Company     Co.  Merchandise  mdse.         Received     Rec'd. 

The  symbol  #  has  two  uses.  5#  means  ''  5  pounds."  #5  means 
"  number  5." 

I.  The  Daybook.  The  following  form  illustrates  the  method 
of  entering  daily  transactions  in  the  daybook. 


^ 


Ot.i.'yaL^^^,   /f/S" 


a47 


VJT 


;/ 


// 


lU 


^        .  ,  / 


^^rr^ 


/^ 


7^ 


^ 


// 


zi^ 


:2^ 


33 


The  numbers  at  the  left  indicate  the  page  in  the  ledger  on  which 
is  recorded  the  individual  account.     (See  Ledger,  p.  177.) 


THE  LEDGER 


177 


It  will  be  observed  by  consulting  the  sample  ledger  page  in  the 
next  illustration  that  this  same  item  is  recorded  only  in  total,  and  that 
the  page  reference  is  ^'247"  or  the  daybook  page  indicated  above. 

II.  The  Ledger.  The  following  form  illustrates  the  method  of 
carrying  to,  or  "  posting  "  transactions  in  the  ledger.  The  illus- 
tration assumes  that  the  charge  in  John  M.  French's  name  is  the 
first  one  on  his  account,  or,  that  he  has  just  "  opened  "  a  new 
account  with  the  merchant. 


45 


J^ 


s 


,Zy^j2..-y^-^>i^C^^^ 


Fr 


So 


/ 


f/U)Uj? 


f^uZ^iyyu^^ 


J 
// 


_^ 


/^ 


/s 

oJ 


/^ 


/^ 


Qu^t^ 


// 


as^Sa^d'/^ 


1. 


if/ 


/a 


^\ 


/V 


£9 


oo 


/^ 


/^ 


The  account  above  has  been  balanced  on  the  last  day  of  the 
month  of  June.  It  includes  other  purchases  made  during  the 
month,  and  on  the  credit  side  it  shows  a  cash  credit  of  $10,  and  a 
labor  credit  of  $5.  Upon  adding  the  amounts  on  the  debit  side 
and  those  on  the  credit  side,  we  find  that  the  debits  amount  to 
$29.16  and  that  the  credits  amount  to  $15.  The  excess  of  the 
debits  over  the  credits  is  $29.16 -$15,  or  $14.16. 


178  BUSINESS  FORMS 

This  amount  is  the  balance  due,  and  to  make  the  totals  on  the 
two  sides  equal,  the  $14.16  is  usually  entered  in  red  ink  on  the 
proper  side.  This  same  balance  is  entered  under  date  of  July  1 
on  the  debit  side,  indicating  that  the  account  of  Mr.  French  starts 
the  month  of  July  with  $14.16  owing  the  merchant. 

WRITTEN   APPLICATIONS 

Make  a  ruled  ledger  form  for  each  of  the  following  accounts, 
supplying  your  own  daybook  page  numbers.  Balance  each 
account  on  the  day  indicated,  using  red  ink  for  the  ruling  and  for 
the  entry  of  the  balance  item. 

1.  Account  with  W.  R.  Shepard. 

June  16,  Dr.,  Mdse.  as  per  daybook  item  in  illustration,  $11.25; 
June  18,  Dr.,  Mdse.,  $1.90;  June  19,  Dr.,  Mdse.,  $4.30;  June  20, 
Dr.,  Mdse.,  $7.91 ;  June  22,  Cr.,  Cash,  $10;  June  23,  Dr.,  Mdse., 
$3.75;  June  24,  Cr.,  Labor,  $4.50;  June  25,  Dr.,  Mdse.,  $6.15; 
June  25,  Cr.,  Produce,  $5.08;  June  26,  Dr.,  Mdse.,  $16;  June  27, 
Cr.,  Cash,  $5;  June  29,  Dr.,  Mdse.,  $11.75;  June  30,  Cr.,  Cash, 
$12. 

Show  that  Mr.  Shepard  owes  a  balance  of  $26.43  on  June  30, 
and  carry  this  balance  to  the  next  month  under  date  of  July  1. 

2.  Account  with  F.  H.  Robbins. 

June  5,  Dr.,  Mdse.,  $5.11 ;  June  7,  Dr.,  Mdse.,  $11.10;  June  8, 
Dr.,  Mdse.,  $57 ;  June  11,  Dr.,  Mdse.,  $21.20 ;  June  15,  Cr.,  Cash, 
$50 ;  June  16,  Cr  ,  Cash,  $12.75  (see  daybook  item  in  illustration) ; 
June  19,  Dr.,  Mdse.,  $32.75;  June  27,  Cr.,  Cash,  $40;  June  30, 
Dr.,  Mdse.,  $17.75;  July  3,  Dr.,  Mdse.,  $35.30;  July  9,  Dr., 
Mdse.,  $54.50;  July  12,  Cr.,  Cash,  $75;  July  14,  Dr.,  Mdse.,  $19. 

Balance  the  account  on  June  30,  and  carry  balance  to  proper 
side  under  date  of  July  1.  Mr.  Robbins  left  town  on  July  15, 
and  made  a  full  settlement  with  the  merchant  on  that  day.  Bal- 
ance the  account  on  that  date  and  find  the  amount  Mr.  Robbins 
paid  to  the  merchant. 


BILLS  179 

3.   Account  with  ^Irs.  J.  A.  Phelps. 

June  4,  Dr.,  Mdse.,  $1.09;  June  5,  Dr.,  Mdse.,  $2.11 ;  June  8, 
Dr.,  Mdse.,  $0.98  ;  June  10,  Dr.,  Mdse.,  $3.05  ;  June  11,  Dr.,  Mdse., 
$1;  June  14,  Dr.,  Mdse.,  $1.10;  June  16,  Dr.,  Mdse.,  $3.33  (see 
daybook  item  in  illustration)  ;  June  21,  Dr.,  Mdse.,  $1.74  ;  June  25, 
Dr.,  Mdse.,  $2.50 ;  June  29,  Dr.,  Mdse.,  $2.06  ;  July  3,  Dr.,  Mdse., 
$1.19;  July  10,  Dr.,  Mdse.,  $6.17;  July  14,  Dr.,  Mdse.,  $0.65; 
July  16,  Dr.,  Mdse.,  $2.47. 

On  July  1  the  merchant  sent  Mrs.  Phelps  a  statement  showing 
the  balance  due  him.  What  was  the  amount  of  that  balance? 
WTiat  was  the  balance  on  July  16?  On  July  17  Mrs.  Phelps 
paid  $20  on  account  and  on  the  25th  she  paid  the  balance.  As 
no  purchases  were  made  after  July  16,  what  amount  was  due  on 
the  25th? 

II.  BILLS 

A  Bill  is  a  detailed  statement  of  indebtedness  for  goods  pur- 
chased or  for  services  rendered. 

Bills  are  usually  presented  on  blanks  printed  for  the  purpose, 
giving  the  name  of  the  firm  presenting  the  bill  and  the  nature  of 
its  business.  The  bill  form  is  filled  in  with  all  the  details  of  the 
purchases,  giving  the  date  of  each  purchase,  the  name  of  each 
article,  the  unit  price  of  each,  the  total  cost  of  each  lot,  and  the 
total  amount  of  the  several  lots. 

As  a  rule  merchants  present  a  bill  immediately  following  a 
purchase,  and  follow  up  the  bill,  if  still  unpaid  at  the  end  of  the 
current  month,  by  a  brief  statement  that  gives  only  the  total 
of  the  whole  bill  or  bills  purchased  during  that  month.  Some 
follow  the  practice,  however,  of  presenting  bills  only  at  the  end 
of  calendar  months,  and  use  statements  only  in  cases  where  their 
bills  have  run  for  some  time. 

It  will  add  to  the  interest  in  this  work  if  sample  bill  forms 
obtained  from  your  local  merchants  are  brought  in  for  study  and 
discussion. 


180 


BUSINESS  FORMS 


A  Bill  is  Receipted  when,  upon  payment,  the  seller  or  merchant 
writes  the  words,  ^'  Received  Payment,"  and  signs  his  name  at 
the  bottom  of  the  bill.  If  some  one  connected  with  the  firm  and 
authorized  to  sign  the  firm  name  receipts  a  bill,  it  is  customary  to 
indicate  this  fact  by  writing  under  the  firm  name  the  signature 
or  the  initials  of  the  person  who  receipted  it.  In  the  illustration 
following  the  bill  is  receipted  by  an  agent  of  the  firm. 


TERMS:  Cash 


PMii  Ai->gi  PuiA      /Hp^  ^p         iffA*^ 


PILLSBURY  FURNITURE  CO. 


DEALERS    IN 


Fine  Furniture,  jrugs  and  Draperies 

Sold  fn        (oJj^f^    ^^^<^^^^U^Jo^^. 


1 


z4d 


//^z 


oo 
o  o 
oo 


oo 


Using  names  suggested  by  the  local  business  in  your  city  make 
out  bills  for  each  of  the  following  apphcations.  In  each  case 
draw  a  billhead,  find  the  total  of  each  bill,  calculate  the  discounts 
where  they  are  given,  and  receipt  each  bill. 


BILLS  181 

WRITTEN   APPLICATIONS 

1.  10 lb.  sugar  at  9j^ ;  15  lb.  rice  at  12^ ;  and  5  lb.  butter  at  58^ 

2.  12  lb.  coffee  at  35^;  50  lb.  sugar  at  S^^;  and  10  lb.  starch 
at  5<^. 

3.  20  yd.  cotton  at  lOji^;  10  yd.  gingham  at  20^;  and  40  yd. 
denim  at  18^. 

4.  18  oranges  at  3^;  48  lemons  at  2^^;  and  60  grapefruit  at 

mi- 

5.  36  bu.  wheat  at  $1.75 ;  45  bu.  oats  at  90^ ;  and  45  bu.  barley 
at  85^. 

6.  34  cans  peas  at  11^;  50  cans  corn  at  12^^;  and  60  cans 
tomatoes  at  16^. 

7.  25  doz.  clothespins  at  4^ ;  12  yd.  toweling  at  15^ ;  and  10  yd. 
muslin  at  9^. 

8.  25  hammers  at  95^ ;  30  chisels  at  60p  ;  12  rip  saws  at  $2.50 ; 
15  back  saws  at  $2.10;  and  18  screwdrivers  at  35^. 

9.  24  blockplanes  at  95^;  30  jackplanes  at  $2.25;  24  try 
squares  at  $1.00;  36  two-foot  rules  at  $1.60  per  dozen;  and  60 
nail  sets  at  $1.25  per  dozen. 

10.  25  yd.  carpet  at  $1.10;  36  yd.  carpet  at  $1.75;  48  yd. 
linoleum  at  $0.75 ;  48  yd.  matting  at  35^ ;  45  yd.  filling  at  50 f^. 
Discounted  at  5%  for  cash.     Find  the  net  amount  of  the  bill. 

11.  A  retail  coal  dealer  bought  110  tons  of  coal  at  $5.10.  Make 
out  a  bill  if  sold  by  the  Lehigh  Coal  Company  to  this  dealer,  allow- 
ing a  discount  of  5%  for  cash,  and  showing  a  receipted  bill. 

12.  Make  out  to  yourself  a  bill  from  your  leading  furniture 
dealer  for  the  following  :  1  dining  room  table,  $45 ;  6  dining  room 
chairs  at  $5.75  each ',  1  bureau,  $65 ;  1  dresser,  $55 ;  1  brass  bed, 
$27.50;  1  box  spring,  $14.50;  1  Wilton  rug,  $52.50;  1  Wilton 
rug,  $42.40 ;  and  30  window  shades  at  $0.75  each.  Discount  the 
bill  at  5%  and  receipt  same. 


182  BUSINESS  FORMS 


RECEIPTS 


In  many  activities  not  strictlj^  commercial  there  is  a  constant 
need  for  the  giving  of  receipts,  and  printed  blank  forms  for  the 
use  of  real  estate  agents,  professional  men,  and  also  for  home  use, 
are  readily  obtained.  A  receipt  should  show  the  name  of  the 
person  or  the  firm  to  whom  it  is  given,  the  amount  received,  the 
date  that  it  was  received,  and  the  signature  of  the  person  or  firm 
who  received  the  payment.  In  addition  some  receipts  provide 
space  in  which  the  nature  of  the  transaction  may  be  written. 
Three  forms  are : 

(1)  The  Cash  Receipt.  This  is  given  either  for  cash  received  on 
account,  or  in  part  payment  of  a  debt;  or  ''in  full  payment'^ 
when  the  whole  of  a  debt  is  paid. 

(2)  The  Rent  Receipt.  This  is  given  for  the  payment  of  rent  at 
fixed  periods  of  time. 

(3)  The  Receipt  for  Service.     Usually  given  for  work. 


Petrnary        1> ^^19 

Lewis  A*  Pugh 


Seventy-five  and  no/lOO ^ ^j/J/t/a^a 


ca4J 


FOT   rent  of  #5240  Wilson  Av.,  fcr  February,  19194 


75  .°£ 


A  variety  of  other  forms  might  be  enumerated.     The  illustra- 
tion shows  a  receipt  given  for  the  payment  of  house  rent. 


THE  PARCEL  POST  183 

WRITTEN    APPLICATIONS 

Draw  a  neat  blank  form  and  fill  out  a  receipt  for : 

1.  $25  on  account.       4.    $40  for  rent.  7.    $75  in  full. 

2.  $3  for  class  dues.     5.    $20  on  account.      8.    |15  for  rent. 

3.  $25  for  service.        6.    $50  for  a  bicycle.    9.    $35  for  service. 

10.  Make  a  receipt  indicating  that  you  have  paid  $20  to  your 
grocer  in  full  of  all  indebtedness  to  him. 

11.  Make  a  receipt  indicating  that  you  have  paid  $10  to  your 
butcher  to  be  applied  on  your  account. 

12.  Make  a  receipt  showing  that  you  have  received  $75  from  a 
tenant  in  payment  of  house  rent. 

13.  Write  a  receipt  indicating  that  you  have  made  a  deposit 
of  $10  with  a  tailor,  in  part  payment  for  a  suit. 

14.  Airs.  Thomas  agreed  to  pay  $5  each  week  on  a  player-piano. 
Write  a  receipt  indicating  that  the  Brunswick  Piano  Company 
received  her  tenth  installment  on  the  debt. 

THE   PARCEL   POST 

Under  the  provisions  of  the  Parcel  Post  it  is  possible  to  send  a 
great  variety  of  articles  by  mail  between  any  two  points  in  the 
L'nited  States.  The  rates  for  this  service  are  governed  by  the 
weight  of  the  article  and  by  the  distance  it  is  carried ;  the  gov- 
ernment has  fixed  certain  limits  of  distance  called  Zones  and  has 
placed  definite  rates  per  pound  for  each  zone. 

The  principal  restrictions  governing  the  service  are : 

(1)  Parcel  Post  matter  must  not  be  of  a  kind  likely  to  injure  any  postal 
employee,  or  to  damage  the  mail  equipment  or  other  mail  matter;  nor 
must  it  be  of  a  character  perishable  within  the  period  reasonably  required 
for  transportation  and  delivery. 

(2)  A  Parcel  Post  package  must  not  exceed  84  inches  in  the  length  and 
the  girth  combined.  *  ,  '^ 


184 


BUSINESS  FORMS 


Zones  and  Rates : 

Parcels  mailed  at  any  office  for  local  delivery  from  that  office 
are  rated  as  local.  For  such  parcels  the  rate  is  5  cents  for  the 
first  pomid  and  1  cent  for  each  additional  two  pounds,  or  fractional 
part  of  two  pounds.  Parcels  mailed  at  any  office  for  dehvery  in 
the  first  or  in  the  second  zone  are  charged  for  at  the  rate  of  5 
cents  for  the  first  pound  and  1  cent  for  each  additional  pound,  or 
fractional  part  of  one  pound. 


TABLE  OF  ZONES  AND  RATES 

Number  op 
Zone 

Distance  in  Miles 

Rate  in  Cents 

First  Pound 

Additional  Pounds 

1&2 
3 
4 
5 
6 
7 
8 

1  to  150 
150  to  300 
300  to  600 
600  to  1000 
1000  to  1400 
1400  to  1800 
over  1800 

5 
6 
7 
8 
9 
11 
12 

1 

2 
4 
6 
8 
10 
12 

The  Limit  of  Weight  for  local  dehvery  and  for  the  first  three 
zones  is  70  pounds.     For  all  other  zones  the  limit  is  50  pounds. 

WRITTEN  APPLICATIONS 

1.  Find  the  cost  of  mailing  a  package  weighing  2  pounds  from 
your  home  to  any  point  in  the  fifth  zone. 

2.  Find  the  cost  of  mailing  a  package  weighing  12-J  pounds  to 
a  point  425  miles  distant  from  your  home. 

3.  The  express  rate  on  a  package  weighing  5  pounds  was  30 
cents  for  a  distance  of  175  miles.  Would  it  cost  more  or  less, 
and  how  much,  to  send  the  same  package  by  parcel  post  ? 

4.  A  wholesaler  sends  out  10  packages  weighing  3  pounds  each 
to  a  town  450  miles  distant,  and  8  packages  weighing  5^  pounds 
each  to  a  town  200  miles  distant.  Find  the  total  cost  of  the 
postage  on  the  18  packages. 


INSURANCE 

Insurance  is  an  agreement  made  by  one  party  to  pay  for  loss 
sustained  by  another  party. 

An  Insurance  Policy  is  the  written  agreement  between  the  two 
parties. 

The  Premium  is  the  amount  paid  for  the  insurance. 

The  Face  of  the  Policy  is  the  sum  payable  by  the  company 
according  to  contract  in  case  of  loss. 

There  are  several  kinds  of  insurance,  the  most  common  and 
important  kinds  being  Fire  Insurance  and  Life  Insurance.  Other 
forms  are  Accident,  Health,  Marine,  Automobile,  Liability, 
Burglar,  and  Plate  Glass  Insurance. 

PROPERTY   INSURANCE 

Fire  Insurance  covers  loss  or  damage  to  property  by  fire,  water, 
smoke,  and  chemicals  used  in  extinguishers. 

The  premium  required  for  a  certain  amount  of  insurance  is 
determined  by  an  application  of  percentage. 

The  amount  of  insurance  which  can  be  carried  on  any  given 
property  is  always  some  fractional  part  of  the  actual  value  of  the 
property. 

Illustration  of  Fire  Insurance. 

Brown  &  Co.  own  an  office  building  worth  $50,000. 

They  insure  the  building  against  loss  or  damage  by  fire,  making 
the  contract  with  the  Franklin  Fire  Insurance  Company. 

The  insurance  company  agrees  to  pay  a  sum  not  to  exceed 
$35,000  in  case  of  total  loss. 

Brown  &  Co.  pay  the  insurance  company  a  premium  of  f  %. 

That  is,  the  insurance  costs  them  annually  .OOfX  $35,000,  or 
$252.50. 

The  problem  of  computing  the  premium  when  the  face  of  the 

policy  and  the  rate  are  given  is  a  simple  application  of  percentage. 

185 


186  lx\SURANCE 

Illustrations : 

1.  Find  the  premium  paid  for  insurance  on  a  property  valued 
at  $4500  at  two  thirds  of  the  valuation,  and  at  a  rate  of  1^%. 

The  phrase,  V^t  two  thirds  of  the  valuation,"  means  that  the  company 
will  return  no  more  than  two  thirds  of  the  actual  value  in  case  of  loss, 
even  though  the  loss  may  be  total. 

.015X|X$4500  =  $45.     Result. 

2.  A  frame  house  is  insured  for  $4500  at  a  3-year  rate  of  .45  per 
$100.     Find  the  premium. 

The  face  of  the  poHcy  being  $4500,  or  "45  hundreds,"  the  premium 
equals 

45  X  $.45  =  $20.25.     Result. 

BLACKBOARD  PRACTICE 

Find  the  premium  when  the  face  of  the  policy  and  the  rate  are, 
respectively : 

1.  $1600,  1%.  7.  $10,000,  li%.  13.  $4500,  1.5%. 

2.  $1800,  li%.  .      8.  $12,000,  2i%.  14.  $12,250,  1.7%. 

3.  $2000,  li%.  9.  $20,000,  2^%.  15.  $15,000,  3.1%. 

4.  $2500,  11%.  10.  $35,000,  2f  %.  16.  $20,000,  2.5%. 

5.  $4500,  lf%.  11.  $40,000,  2^%.  17.  $30,000,  1.6%. 

6.  $7500,  2i%.  12.  $56,000,  lf%.  18.  $35,000,  2.5%. 

Find  the  premium  when  the  face  of  the  policy  and  the  rate  per 
$100  are, 

19.  $8000,  $.40.  23.  $10,000,  $1.10.  27.  $21,000,  $1.05. 

20.  $9000,  $.60.  24.  $12,500,  $1.12.  28.  $25,000,  $1.10. 

21.  $9400,  $.75.  25.  $20,000,  $1.50.  29.  $30,000,  $1.20. 

22.  $9600,  $.90.  26.  $24,000,  $1.35.  30.  $37,500,  $2.25. 


PROPERTY  INSURANCE  187 

WRITTEN   APPLICATIONS   OF   PROPERTY  INSURANCE 

1.  Find  the  cost  of  insuring  a  house  for  $3000,  for  3  years,  at 
60  cents  per  $100  for  that  time. 

2.  A  frame  house  with  a  shingle  roof  is  insured  for  $2500,  for 
3  years,  at  a  rate  of  60  cents  for  that  time.  Find  the  premium 
paid. 

3.  A  similar  frame  house  with  a  slate  roof  is  insured  for  $2500, 
for  3  years,  at  a  rate  of  45  cents  for  that  time.  Find  the  premium 
paid. 

4.  Compare  in  examples  2  and  3  the  cost  of  insuring  the  two 
houses,  one  of  which  had  a  better  roof  protection  than  the  other 
had.  What  is  the  increase  in  per  cent  in  the  premium  because  of 
the  poorer  roof? 

5.  A  merchant  pays  an  annual  premium  of  $240  for  insurance 
on  his  stock  of  goods,  and  the  rate  is  $2  per  $100.  What  is  the. 
amount  of  the  insurance  he  carried  ? 

6.  A  dwelling-house  is  insured  for  f  of  its  value,  for  3  years, 
and  the  rate  is  45  cents  per  $100  for  that  time.  The  value  of  the 
house  is  $12,000.     Find  the  annual  cost  of  the  insurance. 

7.  A  wooden  house  is  insured  for  $4000  at  a  rate  of  If  %,  and 
a  brick  house  is  insured  for  the  same  sum  but  at  a  rate  of  1^%. 
Find  the  difference  between  the  annual  premiums  paid  for  the 
insurance. 

8.  A  factory  valued  at  $20,000  was  insured  for  f  of  its  value  at 
a  2%  rate.  The  insurance  had  run  five  years  when  the  building 
was  totally  destroyed  by  fire.  What  was  the  difference  between 
the  total  of  the  premium  collected  and  the  amount  paid  to  the 
insured  ? 

9.  The  insurance  on  a  new  high  school  building  valued  at 
$250,000  was  written  at  the  rate  o^  $10.35  per  $1000  for  a  term  of 
five  years.  The  risk  was  divided  equally  among  five  different 
companies.  What  premium  did  each  company  receive  for  the 
term? 


188  INSURANCE 

LIFE   INSURANCE 

Life  Insurance  is  an  -agreement  between  an  individual  and  a 
company,  whereby  the  individual  pays  a  certain  amount  to  the 
company  at  stated  periods  and  the  company  agrees  to  pay  a 
stipulated  sum  to  him  or  to  his  heirs,  or  to  a  beneficiary  named  in 
the  policy. 

The  Policy  is  the  written  agreement  provided  by  the  company. 

The  Face  of  the  Policy  is  the  amount  the  company  agrees  to  pay. 

The  Insured  is  the  individual  with  whom  the  company  makes 
the  agreement. 

The  Premium  is  the  amount  paid  by  the  insured  to  the  company. 

The  Beneficiary  is  the  person  who  receives  the  face  of  the  policy 
under  the  conditions  named  in  it. 

The  Ordinary  Life  Policy  provides  that  Ihe  insured  shall  pay 
a  fixed  premium  to  the  company  annually,  semi-annually,  or 
quarterly,  during  the  whole  of  his  life.  In  return  the  company 
pays  the  face  of  the  policy  to  the  beneficiary  at  the  death  of  the 
insured.  The  beneficiary  is  named  in  the  policy,  and  may  be  his 
estate  or  a  person  or  persons  named  by  the  insured. 

The  Endowment  Policy  provides  that  the  insured  shall  pay  a 
stated  premium  as  in  the  case  of  the  ordinary  life  poHcy,  but  these 
premiums  are  limited  to  a  certain  number  of  years.  If  the  in- 
sured lives  to  pay  all  of  the  premiums  required,  the  policy  is  said 
to  mature,  and  the  company  will  return  to  him  the  face  of  the 
policy,  together  with  an  additional  amount  which  has  accumulated 
through  interest  during  the  term  of  payment.  This  form  of  policy 
usually  gives  the  insured  two  options  at  maturity.  He  may  accept 
the  face  with  interest,  as  already  explained,  or  he  may  permit 
the  policy  to  remain  in  force  under  an  agreement  that  the  face 
plus  interest  and  a  share  of  the  company's  profits  shall  be  paid 
to  his  estate  at  his  death,  or  to  the  beneficiary  named  in  the 
policy. 


LIFE  INSURANCE 


189 


The  Limited-payment  Life  Policy  provides  that  the  insured 
shall  pay  a  stated  premium  for  a  certain  number  of  years,  after 
which  the  face  of  the  policy  remains  in  the  possession  of  the  com- 
pany until  paid  to  the  beneficiary  at  the  death  of  the  insured. 
The  phrase,  "  15-payment  life,"  means  that  the  insured  must  make 
fifteen  consecutive  annual  payments,  and  that  his  obligation  to 
the  company  is  filled  upon  making  the  fifteenth  annual  payment. 

The  premiums  charged  by  insurance  companies  for  life  insurance 
are  based  upon  accurate  estimates  of  the  time  a  healthy  person 
of  a  given  age  may  be  expected  to  live.  These  estimates  have 
been  reached  by  investigating  hundreds  of  thousands  of  actual 
cases,  and  by  men  especially  trained  for  this  kind  of  investigation. 
The  insurance  companies  provide  their  agents  with  tables  of 
premiums  charged  for  various  kinds  of  policies  at  different  ages,  and 
the  premiums  given  in  these  tables  are  the  charges  per  SIOOO  of 
insurance.  The  following  table,  suppHed  by  a  prominent  com- 
pany, gives  the  premiums  on  different  kinds  of  policies  at  certain 
ages. 

Annual  Cost  of  Life  Insurance 


Age 

Ordinary  Life 

20-Payment  Life 

20-Year  Endowment 

20 

$18.01 

$27.78 

$47.54 

21 

18.40 

28.21 

47.67 

22 

18.80 

28.65 

47.72 

23 

19.23 

29.10 

47.81 

24 

19.68 

29.59 

47.91 

25 

20.14 

30.07 

48.03 

26 

20.64 

30.58 

48.14 

27 

21.15 

31.12 

48.27 

28 

21.69 

31.87 

48.41 

29 

22.26 

32.23 

48.55 

30 

22.85 

32.83 

48.71 

35 

28.35 

36.17 

49.75 

40 

30.94 

40.34 

51.39 

46 

37.09 

45.69 

54.15 

190  INSURANCE 

Using  the  Table. 

Illustration : 

At  the  age  of  24  a  young  man  took  a  policy  for  $3000,  at  the 
ordinal-y  life  rate.     How  much  must  he  pay  annually  for  the  policy  ? 

From  the  table,  under  "Ordinary  Life"  and  opposite  the  age  line  "24," 
we  find  the  rate  per  $1000,  or  $19.68 

Henoe,  he  must  pay  :  3  X $19.68  =$59.04.     Result. 

WRITTEN   APPLICATIONS 

Find  the  annual  premium  on  each  of  the  following  policies; 
the  kind  of  policy ;  its  face ;  and  the  age  of  the  applicant  being : 

1.  Ordinary  Life :  $2000,  25  years. 

2.  20-year  Endowment :  $3000,  25  years. 

3.  Ordmary  Life  :  $5000,  30  years. 

4.  20-payment  Life  :  $8000,  25  years. 

5.  20-year  Endowment :  $10,000,  30  years. 

6.  20-payment  Life  :  $5000,  35  years. 

7.  20-year  Endowment :  $2000,  20  years. 

8.  Ordinary  Life  :  $3000,  40  years. 

9.  Ordinary  Life :  $3000,  30  years. 

10.  20-year  Endowment :  $3000,  30  years. 

11.  20-payment  Life  :  $10,000,  45  years. 

12.  20-payment  Life  :  $15,000,  40  years. 

(In  the  following  exercises  use  the  table  of  rates  unless  rates 
are  given.) 

13.  A  premium  of  $30.94  annually  was  paid  for  a  15-payment 
life  pohcy  of  $1000.  At  the  end  of  the  term  what  amount  had  the 
insured  paid  for  his  protection  ? 

14.  After  paying  12  annual  premiums  of  $44.70  on  an  insurance 
policy  for  $2000,  the  insured  died.  What  amount  had  he  paid 
for  the  $2000  turned  over  to  his  family  by  the  company  at  his 
death? 


LIFE  INSURANCE  191 

15.  A  man  took  out  a  policy  for  S2000  on  his  30th  birthday 
anniversary,  paying  $76.40  premium  for  a  15-payment  Kfe  poHcy. 
If  the  man  died  in  his  65th  year,  show  approximately  the  profit 
to  the  insurance  company  through  holding  the  premiums  for  the 
long  period  of  35  years,  figuring  interest  at  4%. 

16.  At  the  age  of  25  a  man  insured  his  life  for  $3000,  taking  a 
20-year  endowment  policy  at  the  rate  given.  At  the  age  of  45 
the  company  paid  him  $4157,  the  increase  over  the  face  of  the 
policy  representing  accumulated  profits.  Disregarding  interast, 
find  the  excess  amount  received  by  the  insured  over  the  total  that 
he  paid  the  company. 

17.  At  the  age  of  30  Mr.  Wilson  took  out  a  20-year  endowment 
policy  for  $3000,  and  at  the  age  of  35  he  took  out  a  20-year  endow- 
ment poHcy  for  $5000.  At  maturity,  both  policies  were  paid  to  him 
by  the  companies  issuing  them.  What  excess  did  he  receive  over 
the  total  amount  he  had  paid  them  in  premiums?  If  accumulated 
profits  in  dividends  had  been  permitted  to  remain  with  the  com- 
panies during  the  endowment  periods,  amounting  in  all  to  $2350, 
what  was  the  approximate  profit  gained  by  him  on  his  invest- 
ment in  insurance? 

18.  At  the  age  of  36  a  gentleman  insured  his  life  for  $10,000, 
taking  out  a  15-payment  life  policy  at  a  cost  of  $41.60  annually 
per  $1000.  He  died  at  50  years  of  age,  leaving  this  $10,000  of  in- 
surance to  be  divided  equally  between  two  daughters.  Compare 
the  amount  the  two  daughters  received  from  the  company  with 
the  amount  which  would  have  been  left  them  had  the  father 
invested  annually  at  4%  simple  interest  the  sum  paid  in  premiums. 
(Observe  that  the  invested  premiums  would  have  been  on  interest 
for  periods  respectively  14,  13,  12,  11,  •••  to  1  year.  These  periods 
added  give  the  total  time  at  which  the  several  premiums  would 
have  been  at  interest.) 


192  TAXES 


TAXES 


The  Federal  Government  must  meet  the  expense  of  salaries 
paid  to  its  officers,  of  army  and  navy  maintenance,  of  pensions, 
4 forestry,  irrigation  projects,  etc. ;  the  State  must  provide  for  its 
official  salaries,  for  general  education,  and  for  various  institutions ; 
and  Cities  and  Towns  must  provide  for  schools,  for  police  and 
fire  protection,  and  for  sewers  and  other  necessary  improvements. 
And,  to  meet  these  financial  needs,  property  owners  are  com- 
pelled to  contribute  annually,  or  at  stated  intervals,  a  certain 
percentage  of  their  property  valuation.  This  sum  is  called  a  tax. 
Hence,  the  definition, 

A  Tax  is  a  sum  demanded  by  a  government  for  its  support, 
for  pubHc  purposes,  or  for  improvements. 

A  Direct  Tax  is  a  tax  levied  upon  a  person  or  upon  the  value  of 
his  property  or  his  business. 

An  Indirect  Tax  is  a  tax  levied  upon  imported  goods,  upon 
liquors,  or  upon  the  manufactured  products  of  tobacco,  etc. 

A  tax  upon  imports  is  called  a  Tariff. 

A  tax  upon  manufactures  is  called  Internal  Revenue. 

Real  Estate  is  fixed  property,  like  land  and  the  structures  built 
upon  it. 

Personal  Property  is  movable  property,  like  money,  bonds, 
mortgages,  live  stock,  merchandise,  etc. 

A  Property  Tax  is  a  tax  levied  on  property  of  any  kind,  real  or 
personal. 

An  Assessor  is  an  officer  who  estimates  and  records  the  value 
of  property  which  is  to  be  taxed. 

The  Assessed  Value  of  a  property  is  the  estimate  of  its  value 
made  by  an  assessor,  or  by  two  or  more  assessors  working  together. 

Property  is  usually  assessed  for  taxation  at  a  figure  considerably  below 
its  actual  value.  No  rules  govern  the  process  and  in  different  localities 
there  may  be  a  wide  variation  in  the  valuation  of  properties  which  have 
the  same  actual  value. 


TAXES  193 

The  Rate  of  Taxation  is  nearly  always  expressed  as  a  certain 
number  of  mills  on  each  dollar  of  valuation. 
The  actual  process  is  illustrated  as  follows : 

Suppose  that  a  property  is  assessed  at  $5000. 

If  the  rate  of  taxation  is  1.4  mills,  this  expression  means  that  a  tax 
of  1.4  mills  is  placed  upKjn  each  dollar  of  valuation,  or,  that  $.14  is  the 
tax  required  on  each  $100  of  value. 

Hence,  the  tax  on  a  valuation  of  $5000,  at  a  rate  of  1.4  miUs,  is 

50  X$.  14  =  $7.00.     Result. 

A  Tax  Collector  is  an  officer  legally  authorized  to  collect  taxes. 
He  usually  receives  a  commission  on  the  total  amount  he  collects. 

A  Poll  Tax  is  a  tax  levied  upon  a  person. 

This  tax  is  no  longer  collected  in  some  states,  while  others  still 
demand  it. 

.Special  Forms  of  Taxation.  Other  forms  of  taxation  which 
come  under  the  head  of  licenses  are  the  privilege  of  running  an 
automobile,  of  selling  liquor,  and  of  keeping  a  dog. 

APPLICATION    OF   THE   PRINCIPLES    GOVERNING   TAXATION 

I.  To  Find  the  Amount  of  a  Tax  when  the  Assessed  Valuation 
and  the  Tax  Rate  are  Known. 

Illustration : 

Find  the  tax  on  property  assessed  at  $3000,  if  the  rate  is  4  mills 

on  $1.00. 

4  mills  on  $1  =  $.004  on  each  dollar. 

Hence  3000  X  $.004  =  $12.00.     Result. 

BLACKBOARD    PRACTICE 

Find  the  amount  of  the  tax  on  an  assessed  valuation  of : 

1.  $1200  at  3  mills.  6.  $5000  at  li  mills. 

2.  $1800  at  3i  mills.  7.  $7500  at  1^  mills. 

3.  $2400  at  4  mills.  8.  $12,000  at  2^  mills. 

4.  $3500  at  4  mills.  9.  $15,000  at  3^  mflls. 

5.  $4000  at  3  mills.  10.  $20,000  at  4^  milk. 


194  TAXES 

II.  To  Find  the  Tax  Rate  When  the  Assessed  Valuation  and  the 
Amount  of  the  Tax  are  Known. 

Illustration : 

Find  the  tax  rate  when  property  assessed  at  $3500  is  taxed  for 

$8.75  is  what  per  cent  of  $3500? 

$8.75-^ $3500  =  .002^.     Hence,  the  rate  is  2i  mills.     Result. 

BLACKBOARD   PRACTICE 

Find  the  tax  rate  when  the  amount  of  the  tax  on : 

1.  $1000  is  $1.50.  6  $5000  is  $12.50. 

2.  $1500  is  $3.00.  7.  $8000  is  $30.00. 

3.  $1800  is  $4.16.  8.  $12,000  is  $50.40. 

4.  $2000  is  $6.00.  9.  $18,500  is  $74.00. 

5.  $2750  is  $8.25.  10.  $20,000  is  $66.00. 

III.  To  Find  the  Assessed  Valuation  when  the  Amount  of  the 
Tax  and  the  Tax  Rate  are  Known. 

Illustration : 

Find  the  assessed  valuation  of  a  property  upon  which  a  tax  of 
$18  Ls  paid  when  the  tax  rate  is  3  mills. 

3  mills  expressed  as  a  percentage,  .3  of  1  %  =  .003. 
Then,  $18.00  is  .003  of  the  assessed  valuation. 

$18.00^.003  =  $6000. 
And,  $6000  is  the  assessed  valuation.     Result. 

BLACKBOARD    PRACTICE 

Find  the  assessed  valuation  when  the  tax  and  the  corresponding 
tax  rate  are,  respectively  : 

1.  $12.00  and  3  mills.  6.  $110.00  and  2.2  mills. 

2.  $15.00  and  3  mills.  7.  $125.00  and  2.5  mills. 

3.  $20.00  and  2  mills.  8.  $137.40  and  3  mills. 

4.  $18.75  and  2^  mills.  9.  $162.50  and  3.8  mills. 

5.  $22.50  and  5  mills.  10.  $171.04  and  3.2  mills. 


TAXES 


195 


IV.   Calculating  the  Amount  of  a  Tax  by  the  Tax  Table. 

In  order  to  reduce  the  labor  of  calculating  a  large  number  of 
tax  ])ills,  assessors  often  make  use  of  a  table  constructed  with  the 
tax  rate  as  a  basis.  By  using  such  a  table  the  labor  is  reduced 
to  simple  addition. 

Tax  Table  —  Based  Upon  a  Tax  Rate  of  1,65  Mills 


Valuation 

Tax      1 

Valuation 

Tax 

Valuation 

Tax 

Valtjation 

Tax 

$1 

$.002 

$10 

$.017 

$100 

$    .165 

$1000 

$  1.65 

2 

.003  ! 

20 

.033 

200 

.330 

2000 

3.30 

3 

.005  I 

30 

.050 

300 

.495 

3000 

4.95 

4 

.007 

40 

.066 

1       400 

.660 

4000 

6.60 

5 

.009 

50 

.083 

i       500 

.825 

5000 

8.25 

6 

.010 

60 

.099 

600 

.990 

6000 

9.90 

7 

.012 

70 

.116 

700 

1.155 

7000 

11.55 

8 

.014 

80 

.132 

800 

1.320 

8000 

13.20 

9 

.015 

90 

.149 

900 

1.485 

9000 

14.85 

Illustration : 

Using  the  table  and  the  rate  1.65,  find  the  tax  on  a  property 

assessed  at  $3750. 

Tax  on  $3000  =  $4.95       (3d  line,  last  two  columns.) 
Tax  on      700=    1.155     (7th  line,  5th  and  6th  columns.) 
Tax  on        50  =      .083     (5th  Une,  3d  and  4th  columns.) 


Adding,  Tax  on  $3750  =  $6,188 
Therefor^,  the  tax  bill  would  be  for  $6.19. 


Result. 


BLACKBOARD    PRACTICE 

Using  the  table  and  the  rate  1.65  mills  on  the  dollar,  find  the 
tax  on  property  assessed  at 


1. 

$750. 

6. 

$1200. 

11. 

S3500. 

16. 

$5600^ 

2. 

$825. 

7. 

$1450. 

12. 

$3900. 

17. 

$6250. 

3. 

$860. 

8. 

$1890. 

13. 

$4250. 

18. 

$7500. 

4. 

$945. 

9. 

$2100. 

14. 

$4600. 

19. 

$8725. 

6. 

$985. 

10. 

$2400. 

15. 

$4825. 

20. 

$9450. 

196  TAXES 

V.  The  Method  of  Determining  the  Tax  Rate  which  will  Raise 
a  Required  Amount  on  a  Given  Assessed  Valuation. 

Illustration : 

A  town  whose  real  estate  is  assessed  at  a  total  valuation  of 

$2,950,000  needs  to  raise  $32,450  for  the  coming  year's  expenses 

and  to  build  a  new  road.     Find  rate  of  taxation. 

$32,450  is  what  per  cent  of  $2,950,000? 

$32,450 -^  $2,950,000  =  .011,  or  1.1%. 
Hence,  the  tax  rate  must  be  11  mills  on  $1.00,  or  $11  on  $1000. 

If  a  poll  tax  is  collected  in  the  town  or  if  the  town  gets  a  share 
of  the  State  tax,  the  conditions  would  be  changed  in  the  fore- 
going problem. 

Suppose  that  this  town  has  1500  male  voters,  from  each  of 
whom  a  poll  tax  of  $1  is  collected ;  and  suppose,  furthermore, 
that  the  State  turns  over  $12,500  of  the  State  tax  raised  for  the 
new  road,  a  portion  of  which  passes  through  this  town.  The  cal- 
culation of  the  tax  rate  will  be  as  follows : 

Amount  of  tax  to  be  raised  $32,450 

Received  from  1500  polls  at  $1  each  $  1500 

Received  from  State  12,500 

Total  amount  received  $14,000       14,000 

Total  amount  to  be  raised  by  tax  $18,450 

Then  $18,450  is  what  per  cent  of  $2,950,000? 

$18,450^  $2,950,000  =  .00625.     Result. 

Hence,  the  tax  raised  must  be  6.25  mills  on  $1. 

In  such  a  ease  the  officials  would  probably  raise  a  tax  of  7  mUls,  and 
the  balance  left  in  the  town  treasury  after  paying  the  year's  running 
expenses  and  the  improvements  would  be  carried  over  to  the  next  year. 

WRITTEN   APPLICATIONS 

1.  A  town  levied  a  tax  of  $3500  on  an  assessed  valuation  of 
$1,400,000.     What  was  the  tax  rate? 

2.  A  village  needs  $4500  for  the  expense  of  its  school  system 
for  one  year.  If  the  assessed  valuation  is  $1,350,000,  what  tax 
rate  is  needed  to  raise  the  $4500? 


T.\XES  197 

3.  A  town  requires  $16,000  for  a  year's  expenses  and  its 
property  valuation  is  $2,700,000.  If  the  State  turns  over  $4000, 
what  tax  rate  is  required  to  raise  the  balance? 

4.  In  a  town  that  levies  a  poll  tax  of  $1  each  on  950  voters 
the  officials  decide  to  raise  $6750.  With  an  assessed  valuation 
of  $1,450,000  what  tax  rate  will  raise  the  balance  required? 

5.  Mr.  Johnson,  a  citizen  in  the  town  in  example  4,  has  prop- 
erty valued  at  $15,000.  What  is  the  amount  of  the  tax  he  pays? 
What  would  he  pay  if  no  poll  tax  were  demanded  in  the  town? 

6.  The  valuation  of  all  the  property  in  a  town  is  $2,157,500, 
the  tax  to  be  raised  amounts  to  $28,500,  and  a  taxpayer,  Mr. 
Raymond,  owns  property  assessed  at  $12,500.  Find  the  tax 
rate  and  the  amount  of  the  tax  Mr,  Raymond  pays. 

7.  If  the  town  in  example  6  collected  a  poll  tax  from  each  of 
its  1250  males,  and  if  the  funds  received  from  the  State  amounted 
to  $7250,  what  would  be  the  tax  levied  upon  the  property  owned 
by  Mr.  Raymond? 

8.  Find  from  your  own  town  officials  or  from  printed  reports 
the  amount  of  the  assessed  valuation  in  your  home  town.  Find 
also  the  amount  of  the  poll  tax,  if  that  tax  is  required,  and  the 
amount  of  State  funds  received.  Then  calculate  the  tax  on  a 
property  valued  at  $10,000. 

9.  If  a  man  owns  property  in  a  town  but  does  not  re.side  there, 
he  pays  the  property  tax  but  no  poll  tax.  Mr.  Swift  owns  property 
worth  $15,000  in  a  town  in  which  he  resides,  and  in  which  he  pays 
a  poll  tax  of  $2.00,  He  also  owns  property  worth  $11,500  in  a 
city  where  the  assessed  valuation  is  $1,750,000,  and  where  $77,000 
is  raised  to  build  a  new  school.  In  each  town  the  tax  rate  is  3| 
mills.     Find  his  total  tax. 


198  MORTGAGES 

10.  Some  states  levy  a  tax  on  property  inherited  from  estates, 
the  rate  of  taxation  depending  upon  the  nearness  of  the  relation- 
ship of  the  heirs  to  the  person  leaving  the  property.  If  the  tax 
on  a  widow's  share  is  2%,  and  on  a  son's  or  daughter's  share  1%, 
what  amount  does  the  state  receive  from  an  estate  worth  $300,000 
if  the  w^idow"  receives  $175,000,  and  the  son  $50,000,  and  if  the 
balance  is  divided  between  two  daughters  ? 

MORTGAGES 
A  Legal  Title  to  a  property  is  the  right  of  possession  given  by  law. 

Illustration : 

A  man  pays  $5000  for  a  house.  He  receives  a  written  document  called 
a  deed  from  the  former  owner,  giving  him  full  possession  of  the  property. 
This  deed  is  recognized  by  law  as  a  title  to  the  property. 

A  Mortgage  is  an  agreement  through  which  the  party  loaning 
money  is  given  a  legal  claim  on  a  property  as  a  security  for  the  loan. 

Illustration : 

John  Farnham  had  $2500,  but  wished  to  buy  a  house  costing  $4000. 
Robert  Barber  loaned  Farnham  $1500,  and  as  security  for  the  loan  Farn- 
ham gave  Barber  a  conditional  conveyance,  or  transfer  of  his  house,  until 
the  loan  should  be  paid.     This  conditional  title  is  called  a  mortgage. 

Interest  on  Mortgages  is  usually  paid  semi-annually. 

Failure  to  make  an  interest  payment  when  due  gives  the  holder 
of  the  mortgage  the  right  to  take  the  legal  steps  that  will  compel 
the  sale  of  the  property.  In  this  way  the  holder  of  the  mortgage 
collects  the  amount  of  money  loaned  and  the  interest  due  upon  it. 

Illustration : 

If  the  interest  on  the  mortgage  given  Barber  is  at  the  rate  of  6%, 
Farnham  must  pay  Barber  annually  6%  of  $1500,  or  $90.  If  Farnham 
should  fail  to  pay  the  interest,  Barber  might  have  the  property  sold  by 
the  sheriff,  whereupon  $1500  of  the  sale  price,  together  with  the  interest 
due  him,  would  be  paid  to  Barber.  The  balance  of  the  sum  received  by 
the  sheriff,  less  all  costs,  would  be  paid  over  to  Farnham. 


BUILDING  AND  LOAN  ASSOCIATIONS  199 

WRITTEN    APPLICATIONS 

1.  A  young  man  saved  $2700  and  bought  a  house  for  $4000. 
If  he  placed  a  mortgage  on  the  property  for  the  difference  between 
his  savings  and  the  purchase  price  of  the  house,  and  if  he  paid 
annually  6%  interest  on  the  loan,  how  much  was  his  annual  interest 
payment  ? 

2.  A  young  man  who  was  paying  $360  annually  for  rent,  bought 
a  house  for  $3500,  paying  $3000  cash  and  borrowing  the  balance 
at  5%.  If  his  own  money  had  been  earning  4%  in  bank,  and  if 
his  expenses  for  taxes  and  repairs  were  $100  annually,  how  much 
did  he  gain  each  year  by  investing  in  the  house? 

BUILDING   AND   LOAN  ASSOCIATIONS 

A  Building  and  Loan  Association  is  an  organization  formed  by  a 
number  of  individuals  for  the  purpose  of  saving.  Such  associa- 
tions are  incorporated  under  the  laws  of  the  state  in  which  they 
do  business,  and  are  protected  by  the  Banking  laws  of  that  state. 

To  become  a  member  of  a  building  and  loan  association  a  person 
agrees  to  save  a  certain  number  of  dollars  each  month.  $1.00  per 
month  buys  a  share  in  the  association,  and  this  share  is  worth  $200 
at  maturity. 

The  savings  of  the  members  of  a  building  and  loan  association, 
added  together  each  month,  are  invested  by  the  association  in 
loans  made  to  the  members  of  that  association ;  these  loans  being 
secured  by  mortgages  held  by  the  association. 

The  profits  of  a  building  and  loan  association  consist  of  the  in- 
terest on  the  investment,  and  the  reinvestment,  of  the  savings  of  its 
members. 

These  profits  are  di\ided  equally  among  the  members,  each  member's 
share  being  in  proportion  to  the  amount  of  money  he  has  saved  in  the 
association,  and  depending  upon  the  time  that  he  has  been  a  member  of  it. 


200  BUILDING  AND  LOAN  ASSOCIATIONS 

When  the  savings  of  a  member,  with  the  interest  that  they  have 
accumulated,  amount  to  $200,  for  each  share  he  holds,  the  stock 
is  said  to  mature. 

Under  the  Pennsylvania  plan  the  time  necessary  for  a  share  to  mature 
is  about  11^  years.  As  a  rule,  the  payment  of  $1.00  per  month  for  138 
months  accumulates  earnings  of  $62. 

If  a  member  has  free  stock,  that  is,  if  he  is  in  the  association 
merely  for  the  purpose  of  saving,  he  gets  $200  at  the  end  of  about 
11^  years,  for  each  $1.00  per  month  that  he  has  invested.  Simi- 
larly, a  monthly  saving  of  $5.00  for  the  same  time  would  amount 
to  $1000. 

If  a  member  is  a  borrower,  that  is,  if  he  gives  the  association  a 
mortgage  on  a  property  he  owns  or  is  buying,  he  pays  $1.00  each 
month  as  dues  for  each  $200  he  borrows,  and  also  $1.00  each  month 
as  interest  on  each  $200,  assuming  the  rate  to  be  6%.  After  he  has 
continued  these  payments  for  about  11|-  years,  the'  loan  is  paid 
by  his  savings. 

The  advantages  of  the  building  and  loan  association  as  a  means 
of  saving  are : 

1.  It  affords  almost  absolute  security  for  the  investment  of  money  in 
the  locality  in  which  the  investor  resides. 

2.  It  affords  the  borrower  the  opportunity  to  buy  a  home  at  any  period 
during  the  hfe  of  his  stock. 

3.  It  pays  a  higher  rate  of  interest,  consistent  with  safety,  than  any 
other  form  of  investment. 

4.  It  gives  an  investor  an  opportunity  to  borrow  money  in  case  of  sick- 
ness or  misfortune. 

5.  It  provides  for  the  retm-n  of  the  investor's  savings,  with  his  share 
of  the  profits  of  the  association,  at  any  time  diu*ing  the  hfe  of  his  stock. 

Because  of  the  wide  variation  in  methods,  it  is  difficult  to  give 
practical  applications  that  will  be  helpful.  You  should  be  able  to 
obtain  from  a  near-by  Building  and  Loan  Association  abundant 
material  for  good  problems. 


STOCKS   AND   BONDS 

A  Corporation  is  a  company,  or  group  of  persons,  authorized 
by  law  to  transact  business  of  a  stated  kind. 

A  Stock  Company  is  an  incorporated  company  whose  capital 
is  represented  by  shares  held  by  different  persons. 

The  Organization  of  a  Stock  Company  or  Corporation  Ls  brought 
about  in  the  following  manner. 

1.  The  persons  forming  the  corporation  agree  to  pay  a  certain  amount 
for  which  they  receive  shares  of  stock. 

2.  The  members,  or  stockholders,  elect  from  their  number  a  Board  of 
Directors  to  have  immediate  charge  of  the  business. 

3.  The  Board  of  Directors  elects  officers  of  the  corporation,  including, 
as  a  rule,  a  President,  a  Secretary,  and  a  Treasurer. 

4.  Application  for  a  charter  is  made  to  a  State  Government. 

The  Capital  Stock  of  a  corporation  is  the  amount  represented 
by  the  total  face  value  of  all  of  the  shares. 

A  Share  of  Stock  is  one  of  the  equal  parts  into  w^hich  the  capital 
stock  of  a  corporation  is  divided.     Thus : 

A  capital  of  $250,000  might  be  divided  into  2500  shares  of  $100  each, 
or  into  5000  shares  of  $50  each. 

A  Stock  Certificate  is  a  statement  issued  by  the  corporation  to 
the  stockholders  showing  the  number  of  shares  owned  by  him, 
the  face  value  of  each,  and  how  the  stock  may  be  transferred. 

A  Dividend  is  a  sum  paid  to  the  shareholders  of  a  company  or 
corporation  out  of  the  earnings  or  the  surplus  of  its  business. 

Preferred  Shares  are  the  shares  upon  which  a  corporation  agrees 
to  pay  a  certain  rate  of  interest.  Such  interest  may  be  paid 
annually,  semi-annually,  or  quarterly,  as  the  directors  may  decide. 

Common  Shares  are  the  ordinary  shares  of  a  company  or  corpo- 
ration, and  carry  no  guarantee  of  dividends. 

An  Assessment  is  a  demand  for  cash  made  upon  the  shareholders 

by  a  corporation  when  poor  business  or  misfortune  brings  a  loss 

instead  of  a  profit. 

201 


202  STOCKS  AND  BONDS 

The  Par  Value  of  a  share  of  stock  is  the  face  value  at  which  the 

share  is  issued  and  originally  sold  by  the  corporation. 

Thus  :  If  a  capital  of  $500,000  is  issued  in  500  shares,  each  share  has 
a  value  of  $100,  and  this  is  called  the  par  value.  If  this  stock  had  con- 
sisted of  10,000  shares,  each  share  would  have  had  a  par  value  of  $50. 

The  Market  Value  of  a  Share  of  stock  is  the  amount  which  can 
be  obtained  from  the  public  sale  of  the  share  at  any  given  time. 

Thus  :  If  a  share  of  stock  originally  issued  at  par  vahie  of  $100  is  sold 
during  a  period  of  prosperous  business  it  may  bring  $110,  and  this  value 
is  the  market  value  of  the  share.  But  during  a  period  of  poor  business 
this  same  stock  might  be  earning  merely  a  fractional  part  of  its  earnings 
during  prosperous  times,  and  in  the  opinion  of  investors  its  market  value 
might  not  be  more  than  $75  per  share.  In  general,  the  market  price  of  a 
share  is  constantly  changing. 

BUYING   AND   SELLING    STOCK 

A  Stock  Broker  is  a  person  whose  business  is  the  buying  and 
selling  of  stock. 

A  Stock  Exchange  is  a  business  institution  which  provides  a 
trading  room  and  the  necessary  clerical  system  for  the  buying  and 
selling  of  stock. 

The  Stock  Exchange  provides  a  natural  channel  through  which 
brokers  publicly  offer  to  buy  and  to  sell  stock  certificates.  Its 
transactions  are  governed  by  fixed  and  rigid  rules,  and  the  prices 
established  are  recognized  as  fair  expressions  of  the  demand  for, 
and  the  value  of,  a  stock.  For  example,  if  a  corporation  is  known 
to  be  doing  a  large  and  profitable  business  its  shares  are  looked 
upon  as  an  excellent  investment.  Consequently  the  demand  for 
them  naturally  grows  and  the  "  bidding  "  by  brokers  results  in 
increased  prices,  just  as  any  increased  demand  for  an  article  usually 
brings  an  advance  in  the  price.  On  the  other  hand,  a  period  of 
jx)or  business  and  decreasing  earnings  makes  a  stock  of  less  value 
to  investors,  and  this  condition  is  reflected  by  a  smaller  demand 
on  the  stock  exchange,  or  by  a  general  desire  to  sell,  which  in- 
evitably lowers  the  market  price. 


BUYING  AND  SELLING  STOCK  .      203 

Stock  Exchanges  are  located  in  all  of  the  larger  cities,  but  the 
New  York  Stock  Exchange  is  the  principal  market  for  securities 
in  the  United  States. 

The  Commission,  or  Brokerage,  charged  for  buying  or  selling 
a  stock  is 

7^  cents  per  share  on  stock  quoted  below        SIO. 
15       "        "        "      "       "  "       between  $10  and  §125. 

20       "        "        "       "       "  "       above      $125. 

Stocks  are  quoted  in  dollars  and  fractional  parts  of  a  dollar  based 
upon  1^  of  a  dollar.  Thus,  a  stock  rising  from  75  to  76  may  be  quoted  at 
each  of  the  fractional  parts  of  a  dollar  represented  in  eighths,  and  the  suc- 
cessive quotations  would  be  75,  75-J,  75^,  75|,  75^,  75f ,  75f ,  75J,  and  76. 

To  buy  100  shares  of  a  stock  quoted  at  $85,  the  purchaser  must  pay  : 

For  the  stock 100X$85    =  $8500 

Plus  the  commission 100X$.15=  15 

Total  cost  to  the  purchaser =  $8515. 

If  this  stock  is  sold  sometime  later  at  $130  per  share  : 

For  the  stock 100  X  $130  =  $13000 

Less  the  commission 100X$.20=         20. 

Total  received  by  the  seller =$12980. 

Stock  Quotations.  The  stock  exchanges  are  open  on  every 
business  day  of  the  year,  and  at  the  close  of  each  session  the  prices 
at  which  stocks  have  been  bought  and  sold  are  furnished  to  the 
newspapers  for  publication.  The  late  editions  of  the  afternoon 
papers  publish  them,  and  they  are  also  published  in  the  morn- 
ing papers  on  the  following  day. 

The  only  fractions  used  in  stock  quotations  are  eighths,  quarters, 
and  halves,  as  already  illustrated.  Large  speculators  buy  shares 
in  lots  numbering  from  one  hundred  shares  up  to  several  thoa^ands, 
and  on  many  active  days  the  total  of  the  transactions  reaches 
well  above  amilhon  shares. 


204 


STOCKS  AND  BONDS 


Stocks  usually  bear  names  which  indicate  their  corporate 
business,  but  brokers  shorten  the  names  for  convenience.  The 
phrase  '*  United  States  Steel  Common  "  is  rarely  heard  in  stock 
exchange  circles,  but  the  briefer  form  "  Steel  common,"  or  "  Steel,'* 
is  constantly  used. 

Less  important  stocks  bear  full  names  in  some  instances,  but 
all  are  frequently  abbreviated.  When  a  broker  speaks  of  buy- 
ing 100  shares  of  Erie  Railroad  Common  Stock  he  speaks  of  "  100 
Erie." 

I.  To  Find  the  Cost  of  a  Number  of  Shares  of  Stock  at  a  Given 
Market  Value. 

Illustration : 

Find  the  cost  of  100  Steel  at  75^. 

The  quotation  75^  means  $75.50. 

The  commission  on  100  shares  =  100  X$.15  =  100  X  $0. 16  =  $15. 

The  cost  of  100  shares  at  $75.50  =  $7550. 

Hence,  the  total  cost  to  the  purchaser= $7550 +$15  =$7565.     Result.^ 

BLACKBOARD   PRACTICE 


Adding  the  broker's  commission,  find  the  cost  of : 


1.  100  Erie  at  45.  13. 

2.  100  Long  Island  at  24.  14. 

3.  200  Atchinson  at  95.  15. 

4.  200  D.  &  H.  at  150.  16. 

5.  200  Reading  at  82|.  17. 

6.  250  Am.  Sugar  at  118.  18. 

7.  100  Pennsylvania  at  59|.  19. 

8.  200  Woolworth  at  112^!^  20. 

9.  300  Tenn.  Copper  at  57f .  21. 

10.  250  Gen.  Elec.  at  175f .  22. 

11.  400  Lehigh  Valley  at  82|.  23. 

12.  300  N.  Y.  Central  at  lOU.  24. 


250  O.  &  W.  at  2^. 
300  Studebaker  at  152f . 
300  Beth.  Steel  at  345^. 
350  C.  F.  &  I.  at  47J. 
350  Elec.  Storage  at  60i. 
400  Am.  Tobacco  at  21  If. 
450  Beet  Sugar  at  66|. 
500  Westinghouse  at  67|. 
600  lU.  Central  at  106^. 
1000  Erie  at  44f . 
1000  Can.  Pacific  at  181|. 
2000  Am.  Loco,  at  70|. 


BUYING  AND  SELLING  STOCK  205 

II.  To  Find  the  Amount  Received  from  the  Sale  of  a  Number 
of  Shares  of  Stock  at  a  Given  Market  Value. 

Illustration : 

Find  the  amount  received  by  the  owner  from  the  sale  of  100 
Erie  at  45f . 

The  quotation  45|^  means  $45.75. 

The  commission  on  100  shares  =  100  X$.  15  =  100  X$.  15  =$15. 

The  broker  sells  100  shares  and  receives  100  X $45.75  =$4575.00. 

Hence,  the  net  amount  received  by  the  owner =$4575. 00— $15  =$4560. 

Result. 

BLACKBOARD   PRACTICE 

Deducting  the  broker's  commission,  find  the  net  amount  re- 
ceived by  the  owner  from  the  sale  of : 

1.  100  Reading  at  81.  13.  400  Union  Pac.  at  MOJ. 

2.  100  Pulhnan  at  167.  14.  400  Texas  Pac.  at  15J. 

3.  100  Seaboard  at  18i.  15.  500  Wabash  at  13^. 

4.  100  Can.  Pacific  at  185.  16.  450  Erie  at  42^. 

5.  200  N.  Y.  O.  &  W.  at  30J.  17.  550  Utah  Copper  at  80. 

6.  200  Pittsburg  Coal  at  35^.  18.  600  N.  Y.  C.  at  101^. 

7.  150  Westinghouse  at  68|-.  19.  700  Atchison  at  106i. 

8.  200  C.  F.  &  I.  at  46^.  20.  800  Pennsylvania  at  59f . 

9.  250  Long  Island  at  23f .  21.  1000  C.  F.  &  I.  at  52i. 

10.  200  Studebaker  at  150i.         22.    2000  Reading  at  80^. 

11.  300  Reading  at  81f .  23.   3000  Am.  Sugar  at  116^. 

12.  350  New  Haven  at  72^.         24.   2500  D.  &  H.  at  150|. 

The  following  list  of  stock  quotations  was  published  at  the  close 
of  business  on  the  New  York  Stock  Exchange  on  August  5,  1915. 
(This  list  includes  only  a  small  part  of  the  entire  hst  in  which 
trading  is  carried  on.  In  an  active  business  day  purchases  and 
sales  are  made  in  from  one  hundred  twenty-five  to  one  hundred 
fifty  different  stocks.) 


206 


STOCKS  AND  BONDS 


Stock  Quotations  —  August  5,  191 5 


American  Ice      .     .     . 
Baldwin  Locomotive   . 
Brooklyn  Rapid  Transit 
Canadian  Pacific     .     . 
Central  Leather      .     . 
Delaware  &  Hudson    . 
Erie      .     .     .     .     .     . 

Lehigh  Valley  .  .  . 
Louisville  &  Nashville 
Missouri  Pacific      .     . 


24  New  York  Central       .     .     .  OOf 

801  Pacific  Mail 36 ^ 

86i  Pennsylvania 107| 

145}  PuUman 152 

43  Reading 149| 

1501-  Texas  &  Pacific 14| 

27 \  Third  Avenue b\\ 

143  \  United  States  Steel      ...  70S 

112  Westinghouse 112^ 

2f  Woolworth 104^ 


BLACKBOARD 

Referring  to  the  quotations  in 
broker's  commission, 

Find  the  cost  of : 

1.  10  Am.  Ice. 

2.  20  B.  R.  T. 

3.  30  D.  &  H 

4.  50  Erie. 

5.  75  Woolworth. 

6.  80  U.  S.  Steel. 

7.  100  Can.  Pac. 

8.  100  Westinghouse. 

9.  100  Leh.  Val. 

10.  lOOPenn. 

11.  100  Tex.  &  Pac 

12.  150  Reading. 

13.  200  Pullman. 


PRACTICE 
the  table,   and  including  the 

Find  the  amount  received  for : 

14.  20  Cent.  Lea. 

15.  40  N.  Y.  C. 

16.  50  D.  &  H. 

17.  75  L.  &  N. 

18.  100  Mo.  Pac. 

19.  100  Woolworth. 

20.  100  N.  Y.  C. 

21.  200  Erie. 

22.  300  Reading. 

23.  500  N.  Y.  C. 

24.  1000  U.  S.  Steel. 

25.  1000  Baldwin. 

26.  1500  Third  Ave. 


BUYING  AND  SELLING  STOCK 


207 


in.    Calculating  Profit  or  Loss  on  Stock  Transactions. 

Stock  purchased  at  a  certain  price  and  sold  later  when  the 
market  price  is  higher  brings  a  profit,  and,  in  like  manner,  stock 
sold  at  a  point  below  the  purchase  price  brings  a  loss.  On  the 
preceding  page  a  brief  list  of  stock  quotations  is  given,  and  quota- 
tions for  the  same  stock  more  than  two  months  later  are  given 
below.  The  pupil  can  readily  find  the  actual  changes  in  market 
price  of  these  several  stocks  during  the  interval  between  August  5 
and  November  10,  1915. 


Stock  Quotations  —  November  lo,  1915 


American  Ice      .     . 
Baldwin  Locomotive   . 
Brooklyn  Rapid  Transit 
Canadian  Pacific     . 
Central  Leather 
Delaware  &  Hudson    . 

Erie 

Lehigh  Valley 
Louisville  &  Nashville 
Missouri  Pacific 


251 
120 

89^ 
185 

581 

14H 

421 

80i 

1201 

8^ 


New  York  Central       .     .     .  102 

Pacific  Mail 33 

Pennsylvania 121 

Pullman 160 

Reading 82 

Texas  &  Pacific 16 

Third  Avenue 62 

United  States  Steel       ...  85 

Westinghouse 68 

Woolworth 113 


BLACKBOARD    PRACTICE 


Referring  to  the  quotations  given  for  August  5  and  for  Novem- 
ber 10,  and  assuming  that  each  lot  of  stock  was  purchased  on 
the  first  date  and  sold  6n  the  second  date,  find  the  profit  or  loss, 
deducting  the  broker's  commission. 


1. 

50  Penn. 

9. 

300  N.  Y.  C. 

2. 

50  Steel. 

10. 

300  B.  R.  T. 

3. 

100  Reading. 

11. 

500  Pullman. 

4. 

100  Ice. 

12. 

800  Pac.  Mail 

5. 

100  Penn. 

13. 

900  Steel. 

6. 

100  L.  V. 

14. 

1000  Erie. 

7. 

200  D.  &  H. 

15. 

1000  L.  &  N. 

8. 

100  Westinghouse. 

16. 

1000  Baldwin. 

208  STOCKS  AND  BONDS 

A  Bond  is  a  formal  written  promise  by  which  a  person  or  a 
corporation  is  bound  to  pay  a  certain  sum  at  a  specified  time. 
Bonds  are  issued  by  corporations  to  provide  money  for  improve- 
ments or  other  business  needs,  and  they  bear  interest  that  must 
be  met  at  stated  times.  They  must  be  paid  when  due,  and  the 
laws  provide  that  failure  to  pay  interest  when  due  gives  the  owner 
the  right  to  sell  the  property  of  the  corporation  issuing  them. 

Corporate  Bonds  are  bonds  issued  by  a  corporation. 

Municipal  Bonds  are  bonds  issued  by  a  city  or  a  town. 

Government  Bonds  are  bonds  issued  by  the  United  States,  or 
by  other  countries. 

Municipal  and  government  bonds  are  not  secured  by  mortgage, 
that  is,  by  a  provision  that  permits  sale  of  property. 

Registered  Bonds  are  bonds  that  are  recorded  by  number  and 
in  the  name  of  the  purchaser,  and  their  ownership  cannot  be 
transferred  from  one  person  to  another  without  registering  the 
fact  of  transfer  on  the  books  of  the  corporation  or  the  government 
which  issued  them. 

Coupon  Bonds  are  bonds  that  bear  small  interest  certificates, 
each  one  of  which  is  a  promissory  note  to  pay  a  certain  sum  at  a 
stated  time.  Banks  make  a  practice  of  cashing  these  coupons 
just  as  they  cash  checks,  the  bank  in  turn  collecting  the  amount 
from  the  corporation  issuing  the  bond. 

Bonds  are  usually  named  in  a  brief  form  that  indicates  the  corporation 
that  issued  them  and  the  interest  rate  they  pay. 

Thus:  United  States  Government  Bonds  bearing  4%  interest  are 
referred  to  as  *'U.  S.  4s." 

New  York  City  Bonds  bearing  4%  interest  are  called  "N.  Y.  City  4s." 

The  student  will  observe  that  a  bond  is  usually  a  better  investment 
than  a  stock.  The  bonds  of  a  corporation  have  first  claim  upon  the 
profits  of  the  business,  and  moreover,  the  bonds  are  usually  secured  by  a 
mortgage  on  the  property  of  the  corporation  issuing  them.  Interest  on  a 
bond  is  promised  at  a  fixed  rate,  while  dividends  on  a  stock  depend  upoa 
business  prosperity,  good  management,  and  such  elements  as  may  change 
at  any  time  and  without  notice. 


BUYING  AND  SELLING  STOCK  209 

IV.  To  Find  the  Number  of  Shares  or  Bonds  a  Given  Sum 
WiU  Buy. 

Illustration : 

When  U.  S.  Steel  is  selling  at  72|^  how  many  shares  can  be 

bought  with  $4337? 

Market  price  of  one  share  =  $72,125 

Broker's  commission  =  .15 

Total  cost  of  one  share  =       $72.28 

Then,  $4337 -^  $72.28  =  60,  the  number  of  shares.     Result. 

BLACKBOARD    PRACTICE 

Using  the  list  of  quotations  given  on  page  207  find  the  number  of 
shares  that  can  be  bought  when  the  buyer  invests : 

1.  $6050  in  L.  &  N.  6.  $12,000  in  Erie. 

2.  $57,175  in  Am.  Ice.  7.  $12,000  in  D.  &  H. 

3.  $6275  in  Third  Ave.  8.  $14,500  in  Reading. 

4.  $17,125  in  Steel.  9.  $16,000  m  Westinghouse. 

5.  $41,000  in  N.  Y.  C.  10.  $20,000  in  Woolworth. 

11.  How  many  U.  S.  4s  selling  at  104^  can  be  purchased  with 
$21,000? 

12.  How  many  Mid  vale  Steel  5s  selling  at  78|  can  be  purchased 
with  $15,700? 

13.  How  many  U.  S.  Steel  4s  selhng  at  105^  can  be  purchased 
with  the  proceeds  from  300  shares  of  Erie  that  were  sold  for  35f 
less  commission? 

V.  To  Find  the  Rate  of  Income  to  be  Derived  from  Investments. 

Dividends  paid  on  stock  and  interest  paid  on  bonds  are  paid 
at  a  certain  rate  per  cent  of  the  par  value. 

I.  Stock  bought  below  par  pays  a  net  income  greater  than  the 
fixed  dividend  rate. 

Suppose  a  stock  is  bought  at  74|,  and  pays  4%  annually. 

The  cost  plus  brokerage  is  $74.50 +$.15  =$74.65. 

The  actual  cash  income  per  share  is  $4.00,  annuall5^ 

The  actual  rate  of  income  is  $4.00 ^$74.65  =5.35%.     Result. 


210  STOCKS  AND  BONDS 

11.  Stock  bought  above  par  pays  a  net  income  less  than  the 
fixed  dividend  rate. 

Suppose  a  stock  is  bought  at  $110,  and  pays  annually  4%. 
The  actual  cost  plus  brokerage  is  $110.00 +$.15  =$110.15. 
The  actual  cash  income  per  share  is  $4.00,  annually. 
The  actual  rate  of  income  is  $4.00-^$l  10.15  =3.63%. 

In  the  case  of  bonds  which  run  for  a  definite  length  of  time  and, 
at  maturity,  are  paid  at  par,  the  net  annual  income  is  affected  by 
the  difference  between  the  par  value  and  the  purchase  price. 

Suppose  a  5%  bond  cost  $103f,  and  had  5  years  to  run. 
The  cost  plus  brokerage  was  $1031  +.15  =$103.53. 

Each  year's  interest  return  was $     5.00 

The  total  interest  received  in  5  years  was 25.00 

The  amount  received  for  the  bond  at  maturity  was       .     .     .       100.00 

Therefore  the  purchaser  received  in  all 125.00 

Hisactualcashprofit  was  $125.00 -$103.53,  or 21.47 

His  actual  annual  cash  profit  on  each  bond  was 4.30 

Hence,  his  annual  interest  return  was 

$4.30^$103.53  =  4.15%. 

These  three  cases  illustrate  the  general  problem  of  determining 
the  rate  of  income  derived  annually  from  a  given  investment. 

Tables  showing  the  different  rates  of  income  derived  from  in- 
vestments made  above  and  below  par  values  are  obtainable  at 
most  brokers'. 

WRITTEN  APPLICATIONS 

Find  the  rate  of  income  on  the  investment  when  the  dividend 
rate  and  the  market  price,  respectively,  are : 

1.  6%,  190.  6.  5%,  $90.  11.  7%,  $140. 

2.  6%,  $120.  7.  U%,  $90.  12.  7%,  $125. 

3.  6%,  $150.  8.  5i%,  $110.  13.  4%,  $84.50. 

4.  6%,  $125.  9.  5^%,  $125.  14.  5%,  $115.50. 
6.  6%,  $105.  10.  6%,  $121.50.  16.  4^%,  $121.75. 


APPLICATIONS  211 

16.  From  which  investment  will  the  buyer  receive  the  greater 
income,  a  5%  stock  bought  at  $140  a  share,  or  a  4%  stock  bought 
at  S120? 

17.  Which  investment  will  pay  the  greater  return,  a  5%  stock 
bought  at  $125  a  share,  or  a  4%  stock  bought  at  $100  a  share? 

18.  120  shares  of  stock  paying  5%  were  sold  at  par  of  $100, 
and  the  money  was  reinvested  in  a  4%  stock  selling  at  $75. 
AMiat  was  the  annual  gain  by  the  change  ? 

19.  200  shares  of  stock  paying  4%  were  sold  at  $10  below  par 
of  SllOO.  If  the  money  was  reinvested  in  a  5%  stock  selling  at 
$75,  find  the  gain  in  annual  income. 

20.  Find  the  total  annual  income  from  150  shares  of  a  7%  stock, 
bought  at  90,  and  200  shares  of  a  4%  stock  bought  at  85.  Which 
of  the  two  investments  pays  the  greater  cash  sum?  Which  of 
them  pays  the  higher  rate  of  interest? 

21.  100  shares  of  U.  S.  Steel  common,  par  value,  $100  a  share, 
were  bought  at  $50  a  share.  If  the  stock  paid  4%,  find  the  actual 
return  on  the  investment,  and  the  per  cent  return  on  the  money 
invested. 

22.  A  man  sold  500  shares  of  4%  stock  that  cost  him  $85  a 
share,  and  reinvested  the  proceeds  in  a  5%  stock  that  cost  him 
$100  per  share.  Find  the  amount  of  the  commissions  on  both 
transactions.     Find,  also,  the  gain  or  loss  in  the  rate  per  cent. 

23.  An  investor  has  an  opportunity  to  buy  a  5%  stock  that  is 
selling  at  a  discount  of  10%,  or  to  buy  a  6%  stock  in  another 
company  at  a  premium  of  $25  per  share.  Wliich  investment 
will  pay  the  greater  return?  Omitting  the  brokerage  charges, 
find  what  actual  difference  there  will  be  in  the  return  if  the  total 
amount  invested  is  $22,500. 


PRACTICAL   APPLICATIONS   OF  ARITHMETIC 
I.    PROBLEMS   IN   THE   HOME 

I.   Keeping  House  Accounts. 

Many  thrifty  and  systematic  persons  keep  a  careful  record  of 
the  expenses  incurred  in  keeping  up  the  home.  The  cost  of  food, 
the  cost  of  fuel,  and  the  cost  of  supplies  for  the  kitchen  are  among 
the  most  important  of  the  home  expenses;  and  the  illustration 
shows  a  practical  method  for  recording  these  particular  expense 
items. 


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Books  providing  the  columns  necessary  for  accounts  of  this 
character  may  be  obtained  at  nearly  all  bookstores,  and  the  num- 
ber of  columns  needed  for  each  page  will  be  determined  by  the 
number  of  items  you  wish  to  record. 

212 


HOUSE  ACCOUNTS  213 

WRITTEN   APPLICATIONS 

1.  Find  the  total  amount  spent  for  each  of  the  different  items 
during  the  week  from  January  1  to  January  7  in  the  illustration. 

2.  Find  the  total  expense  for  each  of  the  seven  days  of  that 
week,  and  the  total  amount  for  the  week. 

3.  Check  the  result  in  the  preceding  example  by  referring  to 
the  totals  found  in  example  1,  and  adding  those  totals. 

4.  Make  a  sheet  ruled  as  in  the  illustration,  and  upon  your 
sheet  tabulate  a  series  of  expenditures  of  your  own.  Find  the 
total  expenses  for  each  day  in  your  record. 

5.  Check  your  own  problem  by  taking  the  total  of  the  expenses 
for  each  item  and  the  total  of  these  sums  for  the  entire  week. 
This  total  should  equal  that  obtained  by  adding  the  daily  totals 
from  example  4. 

n.   Division  of  Income  for  Living  Expenses  and  Savings. 

Thrifty  persons  are  careful  to  regulate  their  expenditures  so 
that  a.  portion  of  the  family  income  is  saved  after  necessary  ex- 
penses have  been  provided  for.  Alany  suggestions  have  been 
published  in  books  and  in  prominent  journals,  and  in  nearly  all  of 
them  we  find  that  a  fixed  sum  should  be  devoted  to  such  necessary 
expenses  as  rent,  food,  clothing,  and  insurance ;  that  another  sum 
should  be  provided  for  the  expenses  of  physician,  dentist,  period- 
icals, and  amusements ;  and  also  that  another  definite  sum  should 
be  saved.  This  plan  of  devoting  certain  fixed  portions  or  sums 
to  definite  items  of  expense  is  called  Arranging  a  Budget. 

Careful  students  of  this  plan  have  suggested  the  following  table 
as  a  practicable  plan  for  a  family  of  four  persons.  At  the  ex- 
treme left  the  table  gives  the  earnings  or  income  of  the  family, 
and  the  other  columns  show  the  percentages  of  that  income  that 
may  reasonably  be  spent  on  living  expenses.  It  will  be  observed 
that  the  item  of  '^  rent  "  varies  but  little,  investigators  having 
determined  that  in  families  of  small  or  moderate  income  the 
percentage  for  that  item  is  practically^  fixed. 


214 


PRACTICAL  APPLICATIONS 


Estimated  Expense  —  Family  of  Four 


Annual 
Income 

Rent 

Food 

Clothing 

Miscel- 
laneous 

Savings 

$1200 
1500 
1800 
2400 
3000 

20% 

20% 
20% 
20% 
20% 

35% 
35% 
30% 
30% 

25% 

15% 
15% 
15% 
15% 
20% 

25% 
25% 
25% 
20% 
15% 

5% 

5% 

10% 

15% 
20% 

From  this  table  we  may  obtain  with  reasonable  accuracy  the 
amounts  a  family  with  a  given  income  may  safely  spend  on  the 
different  items  of  living.  Such  a  table  would  fail  in  application 
to  large  incomes,  for  rent  and  food  expense  would  not  continue 
in  the  same  ratio,  and  saving  of  greater  percentages  would  be 
possible. 

Using  the  Table. 

Illustrations : 

A  man's  annual  salary  is  $1200.  What  amounts  can  he  afford 
to  spend  upon  rent,  food,  clothing,  and  miscellaneous  expenses, 
and  what  amount  should  he  save? 

Referring  to  the  table  under  salary  of  $1200, 

For  rent,  20%o  of  $1200  =  $240. 

For  food,  35  %  of  $1200  =  $420. 

For  clothing,  15%  of  $1200  =$180. 

For  miscellaneous  expense,  25%  of  $1200  =  $300. 
Amount  saved,  5%  of  $1200  =  $60. 

(The  work  is  checked  by  adding  the  total  expenses  and  the  savings. 
$1200.) 

In  using  the  table  for  cases  in  which  the  salary  does  not  exactly  corre- 
spond to  the  given  figures  take  the  nearest  lower  salary.  Thus,  in  work- 
ing with  a  given  salary  of  $2000  use  the  figures  for  the  salary  of  $1800. 

Tables  which  extend  beyond  that  given  are  readily  obtained,  but  the 
relative  per  cents  change  as  the  annual  income  increases. 


COST  OF  OWNING  AND  RENTING  A  HOUSE         215 

WRITTEN    APPLICATIONS 

Based  upon  the  percentages  in  the  table,  find  the  amounts  which 
may  reasonably  be  spent  on  the  different  items  when  the  family 
income  is : 

1.  $1200.  5.  $1300.  9.  $2000.  13.  $2700. 

2.  $1500.  6.  $1400.  10.  $2200.  14.  $2800. 

3.  $1600.  7.  $1600.  11.  $2400.  15.  $3000. 

4.  $1800.  8.  $1700.  12.  $2500.  16.  $3500. 

III.   The  Cost  of  Owning  a  House  and  the  Cost  of  Renting  One. 

The  relative  cost  of  owning  or  renting  a  house  is  a  common 
problem.  As  a  great  many  considerations  enter  into  both  sides 
of  such  a  question,  it  is  impossible  to  give  a  general  statement 
which  will  apph^  in  all  cases.  However,  we  may  illustrate  the 
process  by  which  a  man  may  determine  the  expense  of  either  plan 
under  given  conditions ;  and  by  following  the  steps  in  the  illus- 
tration the  student  can  readilv  make  a  reasonablv  accurate  solu- 
tion  of  a  given  problem. 

Illustration  : 

A  young  man  can  buy  a  house  for  $4000,  or  rent  it  for  $30  a 
month.  The  annual  expense  of  owning  it  will  include,  if  he  pays 
for  it  in  full,  taxes,  $30;  insurance,  $8;  water,  $18;  and  repairs, 
$25;  total,  $81. 

For  this  illustration  we  will  assume  that  the  young  man  has 
$4000  in  cash  invested  in  a  savings  fund  which  pays  him  4%. 

Case  1.     Suppose  he  pays  cash  for  the  property. 

To  own  the  house  and  "carry"  it  1  year  will  cost : 

Interest  on  his  money  invested  in  the  house    .     .     .  $160 

Carrying  expense 81 

Total  annual  expense $241 


216  PRACTICAL  APPLICATIONS 

Case  2.  Suppose  he  paj^s  $2500  cash,  and  gives  a  mortgage 
for  $1500  at  6%- 

To  own  the  house  and  "carrj-"  it  1  year  will  cost : 

Interest  on  his  own  money  invested  in  the  house      .  $100 

Interest  on  borrowed  money 90 

Carrying  expense ' 81 

Total  annual  expense $271 

Case  3.     Suppose  he  pays  SIOOO  cash,  and  gives  a  mortgage 

for  $3000  at  6%. 

To  own  the  house  and  carry  it  1  year  will  cost : 

Interest  on  his  own  money  invested  in  the  house      .  $  40 

Interest  on  borrowed  money 180 

Carrying  expense 81 

Total  annual  expense $301 

If  he  rents  the  house  the  annual  cost  will  be  12  X  $30  =  $360.00. 

We  may  conclude,  therefore,  that 

The  saving  if  owned  clear  of  debt  is  $360 -$241  =$119. 

The  saving  if  owned  on  a  small  mortgage  is      $360— $271  =$89. 
The  saving  if  owned  on  a  large  mortgage  is      $360  —  $230  =  $59. 

It  is  difficult,  if  not  impossible,  to  reach  exact  conclusions  in 
such  comparisons,  but  it  appears  that  owning  a  small  property 
clear  of  debt  or  with  a  small  mortgage  is  a  means  of  considerable 
saving.  The  following  problems  should  be  discussed  by  the  class, 
and  much  interest  may  be  created  if  the  pupils  bring  actual  cases 
for  illustration. 

WRITTEN   APPLICATIONS 

1.  Find  the  annual  cost  of  owning  a  house  valued  at  $5000,  if 
money  is  worth  4%  and  if  the  cost  of  maintaining  the  house 
amounts  to  $110. 

2.  Find  the  annual  cost  of  owning  a  house  valued  at  $5000,  and 
upon  which  there  is  a  mortgage  of  $2000  at  5%;  the  owner's 
money  being  worth  3^%,  and  the  cost  for  taxes,  insurance,  and 
repairs  being  $90. 


COST  OF  FURNISHING  A  HOUSE  217 

3.  A  family  rented  a  house  for  a  year  at  $40  monthly,  and  then 
bought  it  for  $5600.  The  money  invested  could  have  been  loaned 
at  5%,  and  the  cost  of  maintaining  the  house  was  $120.  What 
amount  was  saved  in  one  year  by  the  change  ? 

4.  A  man  owns  a  home  costing  $5600,  and  has  on  it  a  mortgage 
of  $2600.  His  annual  carrying  charges  are  $280.  If  his  money 
now  invested  was  in  a  bank  at  5%,  and  if  he  rented  the  house  for 
$40  a  month,  how  much  would  he  save  in  one  year? 

5.  A  family  rented  a  city  house  for  $50  monthly,  and  finally 
moved  into  a  new  house  in  a  suburb  on  which  they  paid  $2500 
cash  and  placed  a  $3500  mortgage  at  5%.  The  annual  taxes  were 
$80 ;  the  water  rent,  $24 ;  and  for  four  years  no  repairs  were 
needed.  Railroad  fares  for  the  family  averaged  $100  annually 
for  the  four  years  they  occupied  the  house.  What  amount  did 
they  save  annually  by  the  change? 

IV.   The  Cost  of  Furnishing  a  House. 

The  cost  of  furnishing  a  house  may  be  divided  between  two  main 
items,  1st,  the  expense  of  putting  the  house  or  apartment  into 
good  condition ;  and  2d,  the  expense  of  the  furniture  and  general 
furnishings. 

WRITTEN   APPLICATIONS 

1.  A  young  man  rented  a  small  house,  agreeing  to  pay  for  all 
necessary  repairs,  and  also  to  pay  $20  per  month  rent.  How  much 
rent  did  he  pay  annually? 

2.  He  painted  the  walls  of  the  kitchen  at  a  cost  of  20(^  per  square 
yard.  The  room  being  12  feet  long  and  12  feet  wide  and  9  feet 
high,  how  much  did  the  painting  cost,  no  allowance  being  made 
for  openings? 

3.  He  papered  four  rooms,  each  15  feet  long,  12  feet  wide,  and 
9  feet  high,  using  paper  that  cost  $0.25  per  single  roll.  How  much 
did  he  pay  for  the  paper,  if  18  strips  were  deducted  for  the 
oDenings  ? 


218  PRACTICAL  APPLICATIONS 

4.  He  finished  the  floor  of  each  of  the  five  rooms  at  a  cost  of 
$0.25  per  square  yard,  and  kalsomined  the  ceihngs  of  all  five 
rooms  at  a  cost  of  $0.10  per  square  yard.  What  was  the  total 
cost  of  finishing  the  floors  and  kalsomining  the  ceilings  ? 

5.  The  furnishings  of  the  kitchen  were :  gas  stove,  $18.75 ; 
table,  $2.25;  tinware  and  utensils,  $21.19;  linoleum,  9  sq.  yd. 
at  $1.25  per  yard ;  and  shades  for  3  windows  at  69^  each.  What 
was  the  total  cost  of  the  kitchen  furnishings? 

6.  The  furnishings  for  the  dining  room  were  a  dining  table 
costing  $28 :  5  chairs  at  $5.75  each ;  1  buffet  at  $42.50 ;  1  serving 
table  at  $21;  glassware  at  $9.25;  4  tablecloths  at  $4.25  each; 
3  dozen  napkins  at  $2.75  per  dozen ;  2  shades  at  $0.90  each ;  and 
a  rug  at  $18.75.     Find  the  total  cost  of  these  furnishings. 

7.  Two  bedrooms  were  furnished  at  exactly  the  same  cost,  one 
in  birch  and  the  other  in  maple.  Each  had  a  chiffonnier  at  $28 ; 
a  bureau  at  $30;  a  brass  bed  at  $21,  with  mattress  at  $13,  and 
spring  at  $7;  2  chairs  at  $3.25  each;  2  window  shades  at  69(z^ 
each ;  and  a  rug  at  $16.75.  Find  the  total  cost  of  the  furnishings 
for  both  bedrooms. 

8.  The  Hving  room  was  furnished  with  a  center  table  at  $25 ; 
3  chairs  at  $7.50  each;  1  chair  at  $11.25;  a  couch  at  $22.50;  a 
rug  at  $21.50;  3  window  shades  at  $.90  each,  and  3  pairs  of  cur- 
tains at  $1.75  each.  Find  the  total  cost  of  furnishing  the  living 
room. 

9.  ^lake  out  a  complete  statement  showing  the  total  amount 
spent  on  repairs  for  each  room ;  the  total  spent  on  repairs  for  all 
the  rooms ;  also  the  total  spent  in  the  furnishing  of  each  room, 
and  a  total  showing  the  whole  amount  spent  for  the  furnishing. 
Give  also  the  total  amount  spent  on  both  repairs  and  furnishing. 
How  much  did  the  young  man  pay  during  the  first  year  for  rent 
and  for  repairs  and  furniture? 


COST  OF  JVIAINTAINING  A  HOME  219 

V.   The  Cost  of  Maintaining  a  Home. 

(a)  Cost  cf  Gas  Lighting. 

Measuring  Gas.  A  gas  meter  records  on  three  dials  the  number 
of  cubic  feet  of  gas  which  passes  into  the  pipes  of  a  house  during 
a  given  period  of  time.  Most  gas 
companies  read  the  meters  once 
each  month,  and  the  difference 
between  two  consecutive  reacUngs 
is  the  amount  of  gas  consumed  during  the  month. 

Reading  a  Gas  Meter.     In  reading  a  gas  meter  observe  that 

1.  Each  division  of  the  dial  at  the  right  represents  100  cubic  feet. 
One  complete  revolution  of  the  hand  on  this  dial  represents  1000  cubic 

feet. 

2.  Each  division  on  the  middle  dial  represents  1000  cubic  feet. 

One  complete  revolution  of  the  hand  on  this  dial  represents  10,000  cubic 
feet. 

3.  Each  division  on  the  dial  at  the  left  represents  10,000  cubic  feet. 
One  complete  revolution  of  the  hand  on  this  dial  represents  100,000 

cubic  feet. 

To  read  the  meter  in  the  illustration,  therefore,  we  note  that 

The  hand  between  1  and  2  on  the  left  dial  means  "10,000  and  more." 
The  hand  between  3  and  4  on  the  middle  dial  means  "3000  and  more." 
The  hand  exactly  on  5  on  the  right  dial  means  "500  exactly." 
Combining  the   three  readings  we  have   10,000+3000+500  =  13,500, 
the  reading. 

BLACKBOARD   PRACTICE 

In  each  of  the  following  examples  let  the  student  draw  upon 
the  board  three  dials  to  represent  the  dials  of  a  gas  meter,  and  let 
him  indicate  the  positions  of  the  hands  for  the  following  readings. 

9.  21,300  cu.  ft. 

10.  22,500  cu.  ft. 

11.  27,600  cu.  ft. 

12.  30,600  cu.  ft. 


1. 

5600  cu.  ft. 

5. 

1000  cu.  ft. 

2. 

8500  cu.  ft. 

6. 

11,900  cu.  ft. 

3. 

9200  cu.  ft. 

7. 

12,500  cu.  ft. 

4. 

9700  cu.  ft. 

8. 

18,700  cu.  ft. 

220  PRACTICAL  APPLICATIONS 

13.  On  July  1  a  gas  meter  registered  12,400  cubic  feet,  and 
on  the  1st  of  August  14,500  cubic  feet.  At  $1.10  per  thousand 
cubic  feet,  what  was  the  cost  of  the  gas  consumed  between  these 
date^  ? 

14.  A  gas  company  presents  bills  at  the  rate  of  $1.10  per  thou- 
sand cubic  feet,  and  then  makes  a  reduction  of  $0.10  per  thou- 
sand if  the  bill  is  paid  within  a  certain  number  of  days.  How 
much  would  this  reduction  take  from  the  monthly  gas  bill  in  the 
preceding  problem? 

15.  The  six  consecutive  monthly  readings  of  a  gas  meter  were 
23,100;  26,800;  29,400;  31,600;  32,500;  and  33,800  cubic  feet 
respectively.  Find  the  amount  of  each  one  of  the  five  bills  when 
the  cost  of  gas  was  $0.80  per  thousand  cubic  feet,  and  also  find  the 
total  amount  of  the  five  bills. 

16.  Find  local  rate  and  solve  problems  14  and  15. 

(6)  Cost  of  Electric  Lighting. 

Electric  current  for  lighting  purposes  is  sold  by  the  thousand 
watts,  the  ''  watt  "  being  the  unit  of  electrical  measurement  for 
electric  power. 

Electric  meters  are  installed  on  the  premises  of  each  consumer, 
and  they  are  read  in  the  same  way  as  the  gas  meter. 

Electric  bulbs  are  made  in  a  great  variety  of  sizes,  the  amount 
of  current  consumed  and  the  amount  of  light  given  depending 
upon  the  size.  The  bulbs  are  classed  according  to  the  amount  of 
current  they  consume  in  one  hour.  Thus,  the  ''50-watt  Hght  " 
consumes  50  watts  of  current  in  1  hour. 

The  common  sizes  of  lights  in  domestic  use  are  the  bulbs  that 
use  10,  15,  25,  45,  and  60  watts  of  current,  respectively. 

The  Amount  of  Current  Used  depends  upon  the  size  of  the  bulb 
and  the  length  of  time  it  is  used. 


COST  OF  ELECTRIC  LIGHTING  221 

Illustration : 

How  much  current  is  consumed  if  a  room  is  lighted  with  2 
45- watt  Hghts  and  4  15-watt  Ughts  for  five  hours ;  and  what  is 
the  cost  of  Hghting  at  10  cents  per  thousand  watts? 

In  5  hr.  2  bulbs  consuming  45  watts  will  use  5  X2  X45  =450  watts. 
In  5  hr.  4  bulbs  consuming  15  watts  will  use  5X4X15  =300  watts. 

Therefore,  the  six  lights  consume  in  aU  750  watts. 

Result. 

The  cost  of  electric  current  is  usually  based  upon  a  stated  charge  for 
each  KXX)  watts  used. 

In  this  case  :        750  watts  =  ^%'V  or  .75  of  1000  watts. 

Hence,  at  lOji  per  1000  watts, 

The  cost  of  750  watts  =  .75  X  $.  10  =  $.075,  Result. 

It  is  common  practice  to  call  1000  watts  a  "  kilo- watt,"  the  prefix  "  kilo  " 
being  derived  from  the  Greek  for  "  one  thousand." 

BLACKBOARD   PRACTICE 

Find  the  numbei  of  watts  consumed  by : 

1.  1  25-watt  lamp  in  3  hours.      3.   3  25- watt  lamps  in  6  hours. 

2.  2  15-watt  lamps  in  4  hours.     4.    5  45-watt  lamps  in  5  hours. 

5.  2  60-watt,  3  25-watt,  and  5  10-watt  lamps  in  4  hours. 

6.  5  25-watt,  8  15-watt,  and  12  10-watt  lamps  in  3  hours. 

7.  If  the  Hghts  in  problem  3  are  used  in  a  grocery  store,  what 
is  the  cost  of  lighting  the  store  on  each  of  the  24  evenings  in  a 
month,  at  $.10  per  kilowatt-hour? 

8.  The  hghts  in  problem  6  are  used  in  a  school  gymnasium 
three  afternoons  a  week  for  ten  weeks,  at  an  average  of  3  hours 
each  afternoon.  What  is  the  cost  of  lighting  this  gymnasium  at 
$.10  per  kilowatt-hour? 

9.  A  family  averages  during  the  month  of  January  the  follow- 
ing light  consumption  In  the  kitchen,  1  45-watt  lamp  for  3 
hours;  in  the  dining  room,  4  25-watt  lamps  for  1  hour;  in  the 
living  room,  1  60-watt  lamp  and  2  25-watt  lamps  for  3  hours; 
and  in  each  of  three  bedrooms,  2  15-watt  lamps  for  one  and  one 
half  hours  each.  At  $.10  per  kilowatt-hour,  how  much  should 
the  hght  bill  for  this  family  amount  to  in  that  month? 


222  PRACTICAL  APPLICATIONS 

(c)  Kitchen  Measures  and  Costs.  Many  housekeepers  calcu- 
late from  time  to  time  the  daily,  monthly,  or  yearly  expense  of 
some  article  of  food.  Such  calculations  enable  them  to  estimate 
in  advance  the  amount  which  may  be  spent  on  a  particular  thing, 
and  the  ''  budget  plan  "  is  often  worked  out  in  this  way. 

WRITTEN  APPLICATIONS 

1.  A  family  uses  daily  2  quarts  of  milk  at  12  cents  a  quart, 
and  ^  pint  of  cream  at  72^  a  quart.  How  much  does  this  family 
spend  for  both  in  the  month  of  April? 

2.  How  many  pounds  of  butter  will  a  family  use  in  90  days, 
3  meals  to  each  day,  if  they  average  a  pound  for  every  eight  meals  ? 

3.  A  farmer's  family'  uses,  on  the  average,  2^  pounds  of  potatoes 
at  each  of  two  meals  daily  from  September  1  to  June  30  following. 
How  many  bushels  of  potatoes  should  the  farmer  raise  for  his  own 
use? 

4.  A  cookbook  directs  that  a  turkey  be  roasted  20  minutes  for 
each  pound  of  its  weight.  At  what  hour  should  a  turkey  weigh- 
ing 9^  pounds  be  placed  in  the  oven  to  be  ready  for  dinner  at  half- 
past  six  o'clock? 

5.  A  family  of  four  persons  uses  two  pounds  of  butter  a  week 
for  1  year.  If  the  average  price  of  butter  during  that  time  is  45^, 
find  the  total  amount  spent  for  butter  by  this  family  during  the  year. 

6.  A  family  used  a  gas  stove  and  a  gas  water-heater  for  six 
months  at  an  average  expense  of  $3.25  per  month.  They  then 
changed  to  a  coal  stove  and  in  six  months  used  4  tons  at  $8  a  ton. 
Which  was  the  more  economical? 

7.  A  housekeeper  preserved  60  cans  of  strawberries,  using  for 
each  can  1  quart  of  berries  and  1  pound  of  sugar.  The  berries 
cost  12^^  a  quart,  the  sugar  S^i  a  pound,  the  cans  lo^  a  dozen, 
and  the  gas  burner  consumed  8  cu.  ft.  of  gas  per  hour  for  5  hours 
at  a  cost  of  90^  per  thousand  cubic  feet.  Find  the  total  cost  of 
the  fruit  when  preserved  and  the  cost  per  can. 


ECONOMY  IN  BUYING  223 

(d)  Economy  in  Buying.  Shrewd  housekeepers  are  careful  to 
purchase  such  staple  articles  as  flour,  sugar,  soap,  etc.,  in  quanti- 
ties, and  many  stores  make  a  practice  of  offering  reductions  in 
such  goods  on  '^  bargain  days."  The  saving  appears  small  at 
first,  but  if  the  practice  is  carried  on  over  any  great  length  of 
time,  it  is  possible  to  save  a  large  amount. 

WRITTEN   APPLICATIONS 

1.  A  large  store  offers  4  pounds  of  the  regular  35-cent  cocoa  for 
$1.10.  If  a  family  uses  regularly  12  pounds  of  cocoa  in  a  year, 
how  much  would  be  saved  by  purchasing  a  year's  supply  at  this 
bargain  rate? 

2.  At  a  grocery  sale  100  cakes  of  laundry  soap  are  offered  for 
$3.25,  the  regular  price  of  the  soap  being  5  cents  per  cake.  How 
much  would  be  saved  by  purchasing  100  cakes  at  this  reduced  rate  ? 

3.  Butter  can  be  purchased  in  20-pound  tubs  at  42  cents  a 
pound,  and  print  butter  at  45  cents.  If  a  family  uses  3  pounds 
of  butter  a  week,  how  much  would  be  saved  in  one  year  by  buying 
the  tub  butter? 

4.  A  grocer  sold  potatoes  at  $1.50  a  bushel,  or  at  40  cents  a 
peck.  How  much  could  be  saved  by  buying  3  bushels  at  the 
first  price  instead  of  purchasing  them  a  peck  at  a  time  ? 

5.  A  dry  goods  store  offers  a  bolt  of  cloth  measuring  45  yards 
for  7^^  a  yard  if  the  whole  bolt  is  purchased.  How  much  would 
a  woman  save  by  buying  it  all  instead  of  purchasing  it  in  small 
pieces  at  8^^  a  yard? 

6.  A  man  bought.  3  tons  of  coal  in  April,  paying  $6.50  a  ton, 
4  tons  in  September  at  $7  a  ton,  and  5  tons  in  December  at  S7.75 
a  ton.  How  much  would  he  have  saved  if  he  had  bought  it  all  in 
April  ? 

7.  A  barrel  of  flour  could  have  been  purchased  for  $15,  but  a 
housewife  bought  it  in  |^-barrel  sacks  at  $1.90  per  sack  whenever 
she  needed  it.  How  much  would  she  have  saved  bv  buvins:  the 
whole  barrel  in  the  beginning? 


224  PRACTICAL  APPLICATIONS 

8.  A  housewife  purchased  100  bars  of  soap  at  $3.15,  2  dozen 
cans  of  corn  at  $2.95,  and  6  pounds  of  coffee  at  $.33  a  pound.  The 
regular  price  of  the  soap  was  b<t-  a  bar ;  of  the  corn,  16^  a  can ; 
and  of  the  coffee,  38^  a  pound.  Find  the  total  amount  she  saved 
by  buying  in  quantity. 

(e)  Menus  and  Their  Costs.  Authorities  on  domestic  science 
have  suggested  various  menus  which  provide  all  of  the  necessary 
food  values,  and  yet  provide  them  at  a  minimum  of  expense. 

WRITTEN   APPLICATION 

1.  What  is  the  cost  of  soup  for  each  of  four  persons  if  a  can  of 
celery  costs  $.10  and  a  pint  of  milk  costs  8  cents? 

2.  A  breakfast  for  four  persons  consists  of  grapes  costing  $.06, 
oatmeal  costing  $.06,  griddle  cakes  costing  $.20,  sirup  costing  $.10, 
butter  costing  $.18,  and  coffee  costing  $.08  and  cream  and  sugar 
costing  $.12.     Find  the  cost  per  person. 

3.  Which  of  the  following  breakfasts  is  the  cheaper  for  a  family 
of  four : 

No.  1 :  Oatmeal,  5^  ;  8  eggs  at  30^  a  dozen ;  ^  lb.  bacon  at  36jzf ; 
pan  of  rolls  at  5^;  coffee  and  sugar  at  6^;  butter  at  12  f^;  cream 
at  8^. 

No.  2 :  Bananas  and  cream  at  15^ ;  buttered  toast  at  lOjzf  ] 
baked  beans  at  20^ ;    and  brown  bread  at  lOc^ ;    butter  at  \2i^. 

4.  A  woman  served  a  luncheon  for  eight  persons  at  the  follow- 
ing cost : 

2  chickens   .     .     .     .     $1.87      Biscuit 30 

Celery 25      Butter 15 

Salad  :  Cocoa 20 

Lettuce    .     ...     .         .08     'Olives 35 

Eggs 20      Ice  cream        70 

Oil 05      Cake 50 

Find  the  total  cost  of  the  luncheon  and  the  cost  per  person. 


MENUS  AND  THEIR  COSTS 


225 


•5.  A  woman  served  cocoa  and  cake  to  twelve  friends,  using 
2  quarts  of  milk  at  8f^ ;  1  cup  of  sugar  at  6^  per  pound ;  and  12 
tablespoonfuls  of  cocoa  at  35^  per  pound.  If  1  cup  of  sugar  weighs 
^  pound,  and  if  1  tablespoonful  of  cocoa  weighs  1  ounce,  find  the 
cost  of  the  cocoa;  and  if  the  cake  cost  50^,  find  the  cost  of  the 
luncheon  per  person. 

6.  A  housewife  served  dinner  to  her  family  of  six  persons  with 
the  following  menu:  steak,  $0.65;  potatoes,  $0.10;  string  beans, 
$0.15;  bread,  $0.05;  butter,  $0.12;  coffee,  $0.06;  and  dessert 
consisting  of  milk,  $0.12;  eggs,  $0.18;  butter,  $0.12;  lemons, 
$0.10;  and  sugar,  5^.     What  was  the  total  cost  of  the  dinner? 

7.  A  school  kitchen  served  a  luncheon  to  sixty  children,  charg- 
ing them  15^  each.  The  menu  consisted  of  tomato  soup,  bread, 
and  butter,  and  tapioca  cream. 

The  soup  cost :  The  tapioca  cost : 

15  cans  soup  stock  at  ISj^  .     $2.70      2  packages  tapioca  at  10^.  .  $.20 

30     tablespoonfuls     butter                    8  quarts  milk  at  8j^     .     .     .  .64 

(15  oz.  at  48{^  per  pound)  .45  I2  dozen  eggs  at  32^  .  .  .48 
8  quarts  milk  at  8^     .     .     .         .64      5  cupfuls   sugar   at   6^   per 

Total  cost       ....     $3.79          pound  (1  cupful  =  ^  pound)  .15 

Vanilla .05 

Total  cost $1.52 

The  bread  and  butter  cost : 

10  loaves  bread  at  5j^ .$0.50 

1^  lb.  butter  at  56^         .M 

Total  cost $1.34 

What  was  the  amount  of  profit  made  by  the  school  ? 

8.  From  a  newspaper  advertisement,  or  from  a  local  grocer, 
obtain  a  list  of  prices  of  various  foods.  Plan  the  breakfast, 
luncheon,  and  dinner  menus  for  a  family  of  six  p>ersons,  and 
estimate  the  cost  of  all  three  meals. 


226 


PRACTICAL  APPLICATIONS 


n.     PROBLEMS    IN    MANUAL    TRAINING 

Estimating  Lumber  Bills  from  Detail  Drawings.  We  have 
learned  under  Practical  Measurements  that  a  detail  drawing  shows 
the  dimensions  of  the  material  used  in  making  an  article.  In  the 
manual  training  room  we  have  constant  need  for  calculating  the 
amount  of  material  needed  for  making  a  thing,  and  this  list  of 
stock  required  is  called  the  Bill  of  Lumber. 


i     t 


15"- 


CO 

1 


Illustration : 

To  estimate  the  bill  of  lumber  needed  for  the  book  rack  shown 
in  the  drawing,  and  to  give,  in  addition,  the  list  of  material  for 
''  assembhng  "  or  putting  the  parts  together,  and  the  material 
required  for  "  finishing." 


LUMBER  BILL 

1  piece|"X6"Xl5"     (Bottom) 
2pieees|"X5"x5"      (Ends) 

To  allow  for  squaring  and  finishing  the  rack  wiU  require  one  board 
Other  material :  4  wood  screws  1|"  long.     Stain.     Wax. 


MANUAL  TRAINING 


227 


WRITTEN  APPLICATIONS 

1.    Find  bill  of  lumber  and  estimate  all  material  necessary  for 
the  knife  and  fork  tray  in  the  detail  drawing. 

1  piece  h"X9"Xlo"  (Bottom)  2  pieces  -^-"X3"Xir)"  (Sides) 

1  piece  V'X5"X  14"  (Partition)       2  pieces  ^"X3"X8"  (Ends) 

Estimate  the  lumber  needed,  as  well  as  the  nails,  the  stain,  and  the  wax 
for  finishing,  and  estimate  the  total  cost  of  the  tray  at  yonr  local  prices. 


15"- 


0) 


[I 


_i_i_ 


CO 


2'.  The  drawings  show  some  of  the  details  of  a  table.  Plan 
the  other  details  and  make  an  estimate  of  the  lumber  bill  based 
on  your  local  prices. 


50'^ 


43"- 


27'- 


20' 


J  4 


o 
C9 


228 


PRACTICAL  APPLICATIONS 


3.  The  estimate  of  a  lumber  bill  for  a  chair  must  provide  for 
the  pieces  given  in  the  list  below.  Calculate  the  cost  of  the  lumber 
if  the  chair  is  made  from  white  oak  costing  $90  per  thousand. 


LUMBER  BILL  FOR  CHAIR 


Front  Legs. 
Back  Legs. 
Side  Braces. 
Front  Braces. 
Rear  Braces. 
Rear  Brace. 
Arms. 


2  pieces. 

2  pieces. 
6  pieces. 

3  pieces, 
2  pieces. 

1  piece. 

2  pieces. 


2''X2"X1'  6" 

2"X2"X2'  6" 

f"X2"Xl4" 

|"X2"X15" 

f"Xli"Xl5" 

f"X2i"Xl5" 

f"X4"Xl6i" 


4.  Plan  the  proportions  and  make  up  the 
lumber  bill  for  the  telephone  stand  shown 
in  the  drawing.  Allow  10%  for  waste  by 
adding  this  allowance  to  the  size  of  the 
finished  pieces. 


The  Construction  of  Shapes  Used  in  Man- 
ual Training  Designs.  Many  of  the  shapes  used  in  the  designing 
of  furniture  may  be  readily  laid  out  or  drawn  on  wood  by  simple 
applications  of  geometry. 

(1)  The  Hexagon.  One  of  the  common  shapes  in  use  is  the 
hexagon,  a  figure  having  six  sides.     To  lay  out  a  hexagon  which 

shall  have  six  equal  sides  of  a  desired  length 
we  proceed  as  follows  : 

1.  Draw  a  circle  with  a  radius  equal  to  the  side 
of  the  desired  hexagon. 

2.  Beginning   at  a  point   on  the  circle,  lay  off 
the  radius  six  times  as  in  the  figure. 

3.  Join  the  six  points. 

(2)  The  Octagon.  If  we  know  the  diameter  of  the  required 
octagon,  or  figure  of  eight  sides,  the  octagon  may  be  constructed 
as  follows : 


MANUAL  TRAINING 


229 


1.  Draw  a  circle  whose  diameter  is  equal  to  the 
length  of  the  diameter  of  the  required  octagon. 

2.  Draw  two  diameters  making  right  angles 
to  each  other  (AE  and  GC). 

3.  Find  the  middle  point  of  the  arc  AC  (B) ; 
the  middle  point  of  the  arc  CE  (D)  ;  the  middle 
point  of  the  arc  EG  (F) ;  and  the  middle  point 
of  the  arc  GA  (//). 

4.  Join  the  eight  points  of  division  on  the 
circle,  and  the  figure  ABCDEFGH  is  the  required  octagon. 


"^^^^ 

'^ 

J 

^ 

B>^:>>^^ 

y- 

WRITTEN  APPLICATIONS 

1.  Construct   a  hexagon  the  length  of  whose  sides  shall  be 
10  inches. 

2.  Construct  a  hexagon  in  a  circle  whose 
radius  is  8  inches. 

3.  Construct  a  hexagon  in  a  circle  whose  di- 
ameter is  12  inches. 

4.  Construct  a  triangle,  all  of  whose  sides 
shall  be  equal,  in  a  circle  whose  diameter  is  10". 
(Hint :  Study  the  figure  obtained  in  problem  1.) 

6.   Construct  a  triangle,  all  of  whose  sid-es  shall  be  ecjual,  in  a 
circle  whose  radius  is  6  inches. 

6.  The  ornamental  figure  at  the 
right  is  often  used  in  furniture  design. 
Observe  the  method  of  construction 
and  then  make  a  similar  figure  by  stai't- 
ing  with  a  circle  whose  diameter  is  5 
inches. 

7.  Study  the  method  by  which  the 
design  at  the  right  is  laid  out,  and  con- 
struct a  similar  design  for  one  of  the 
legs  of  a  taboret.  Assume  the  width  of 
the  legs  to  be  8  inches,  and  allow  a  mar- 
gin of  1  inch  on  each  side  of  the  design. 


230 


PRACTICAL  APPLICATIONS 


8.  The  figure  at  the  left  shows  the 
dimensions  of  one  of  the  four  sides  of 
a  waste-basket.  If  the  bottom  of  the 
basket  is  to  be  square  and  if  two  of 
the  sides  are  to  be  set  in  between  the 
other  two,  find  the  dimensions  of  the  two 
smaller  sides.  Calculate  the  lumber  bill 
for  the  basket,  using  half -inch  stock,  and 
estimate  the  cost  at  $75  per  thousand 
for  the  lumber. 

(Study  the  figure  at  the  left  in  order  to  determine  the  shapes 
needed.) 

9.  Calculate  the  lumber  bill  necessary  for  a  taboret  whose  top 
is  hexagonal  shape  12  inches  in  diameter,  and  whose  three  legs  are 
made  of  inch  stock  and  15  inches  high.  For  the  3  braces  use 
inch  stock  2  inches  wide. 


Review.     Find  the  total  area  of  each  of  the  following. 


Find  the  area  of  the  shaded  portion  of  each  of  the  following 
figures : 


ADDITIONAL   TOPICS   FOR    STUDY  AND 

REFERENCE 


MEASUREMENT    OF    SOLIDS 

A  Solid  has  three  dimensions,  length,  breadth,  and  thickness. 
A  Polygon  is  a  plane  figure  bounded  by  straight  lines. 
Polygons  are  named  according  to  the  number  of  sides. 

The  triangle  is  a  polygon  having  three  sides. 

The  square  is  a  polygon  having  four  equal  sides  and  four  right  angles. 

The  rectangle  is  a  polygon  ha\'ing  right  angles  and  its  opposite  sides 
equal. 

These  three  polygons,  the  triangle,  the  square,  and  the  rectangle,  are 
special  and  exceedingly  common  forms  of  polygons. 

A  pentagon  is  a  polygon  having  five  sides. 

A  hexagon  is  a  polygon  having  six  sides. 

An  octagon  is  a  polygon  ha^dng  eight  sides.* 

Similar  Polygons  are  polygons  that  have  exactly  the  same  shape. 

Similar  polj^gons  are  not  necessarily 
equal  in  size. 

The  two  triangles  in  the  figure  are  simi- 
lar for  the  shape  is  the  same  in  both. 


A  Prism  is  a. solid  whose  ends  are  equal 
and  similar  polygons  in  parallel  planes,  and 
whose  faces  are  parallelograms. 

The  solid  at  the  right  has  two  equal  and 
similar  polygons  ABC  and  DEF  for  bases, 
these  bases  being  parallel ;  and  the  faces 
ADFC,  CFEB,  and  BE  DA  are  parallelo- 
grams.   Prisms  are  named  from  their  bases. 

231 


232 


MEASUREMENT   OF   SOLIDS 


Types  of  Prisms 
(a)  is  a  triangular  prism.  (c)   is  a  pentagonal  prism. 

(6)  is  a  rectangular  prism.  (d)  is  a  hexagonal  prism. 

The  Altitude  of  a  Prism  is  the  perpendicular  distance  between 
the  bases. 


M 


The  Lateral  Area  of  a  Prism  is  the  area  of 
the  surface  formed  by  the  parallelograms.  ^^^ 

The  lateral  area  of  a  prism  is  easily  illus- 
trated in  the  figures  at  the  right. 


(b) 


In  (a)    a  rectangular  area  is  divided  into 
three  parts  by  the  lines  CD  and  MN. 

In   (6)  the  original  area  is  partly  folded 
upon  the  lines  CD  and  MN. 

In   (c)   the  folding  is  completed  and  the    '•'^^ 
extreme  edges  of  the  original  area  are  brought 
together  on  the  edge  AB. 

Thus  the  parallelograms  have  inclosed  a  solid,  and  the  lateral 
area  of  this  solid  is  the  sum  of  the  areas  of  these  parallelograms. 

The  Total  Area  of  a  Prism  is  the  sum  of  the  lateral  area  and  the 
areas  of  the  two  bases. 


MEASUREMENT  OF  SOLIDS 


233 


If  two  triangles  ACM  and  DB  N, 
in  which  two  sides  equal  respec- 
tively the  ends  of  the  outside  rec- 
tangles, are  folded  into  the  solid 
as  in  (d),  the  total  area  of  the 
soHd  will  be  the  sum  of  these 
triangles  and  the  lateral  area. 


M 


e 


N 


BLACKBOARD   PRACTICE 

Find  the  lateral  area  of  a  rectangular  prism  when  the  perimeter 
of  the  base  and  the  altitude  are,  respectively  : 

1.  5  in.,  7  in.  6.   2  ft.  9  in.,  3  ft.     11.   12  ft.  6  in.,  G  ft. 

2.  10  in.,  12  in.       7.   3  ft.  6  in.,  4  ft. 

8.  3  ft.  8  in.,  oft. 

9.  5  ft.  2  in.,  7  ft. 
10.  8  ft.  5  in.,  9  ft. 


3.  12  in.,  15  in. 

4.  16  in.,  20  in. 

5.  18  in.,  21  in. 


12.  15  ft.  4  in.,  6  ft. 

13.  18  ft.  8  in.,  4  ft.  6  in. 

14.  18  ft.  10  in.,  5  ft.  8  in. 

15.  21ft.  11  in.,  9  ft.  3  in. 


Find  the  lateral  area  of  a  square  prism,  when  one  base  edge  Lnd 
the  altitude  are,  respectively  : 

16.  7  in.,  10  in.  20.  1  ft.  9  in.,  20  in. 

17.  9  in.,  15  in.  21.  2  ft.,  2  ft.  5  in. 

18.  12  in.,  18  in.  22.  3  ft.,  4  ft.  6  in. 

19.  15  in.,  20  in.  23.  5  ft.  8  in.,  8  ft. 


24.  4  ft.,  15  ft.  6  in. 

25.  6  ft.,  18  ft.  10  in. 

26.  7  ft.  6  in.,  21  ft. 

27.  8  ft.  4  in..  35  ft. 


Find  the  total  area  of  a  rectangular  prism,  when  the  dimensions 
of  the  base  and  the  altitude  are,  respectively  : 


28.  9  in.  by  10  in.,  3  ft. 

29.  10  in.  by  12  in.,  4  ft. 

30.  1  ft.  by  1  ft.  3  in.,  3  ft. 

31.  3  ft.  by  2  ft.  4  in.,  4  ft. 

32.  4  ft.  6  in.  by  2  ft.,  7  ft. 

33.  4  ft.  10  in.  by  8  in.,  6  ft 

34.  5  ft.  by  3  ft.  2  in.,  4  ft. 


35.  2  ft.  3  in.  by  3  ft.  1  in.,  4  ft.  6  in. 

36.  3  ft.  8  in.  by  2  ft.  7  in.,  5  ft.  9  m. 

37.  4  ft.  7  in.  by  3  ft.  1  in.,  4  ft.  4  in. 

38.  6  ft.  6  in.  by  4  ft.  4  in.,  9  ft.  6  in. 

39.  6  ft.  9  in.  by  5  ft.  1  in.,  10  ft.  4  in. 

40.  8  ft.  3  in.  by  4  ft.  8  in.,  11  ft.  9  in. 

41.  9  ft .  8  in.  by  3  ft.  11  in.,  10  ft .  3  in. 


234 


MEASUREMENT   OF   SOLIDS 


The  Volume  of  a  Prism  is  the  measure  of  the  prism  in  cubic  units. 
We  found  that  the  vokmie  of  a  rectangular  sohd  equals  the  con- 
tinned  product  of  its  length,  breadth,  and  thickness, 
all  expressed  in  the  same  units  of  measure.  In  the 
figure  the  base  is  three  units  long  and  two  units 
wide,  and  the  solid  is  four  units  high.  Therefore, 
its  volume  is  made  up  of  as  many  cubic  units  as 
there  are  in  the  product  of  3x2x4,  or  24  cubic 
units. 

In  general,  therefore. 

The  volume  of  a  prism  is  equal  to  the  product  of  its  altitude  and 
the  area  of  its  base. 

BLACKBOARD    PRACTICE 


Find  the  volume  of  a  prism  whose  base  area,  and  altitude,  respec- 
tivelv.  are : 


1.  10  sq.  in.,  5  in. 

2.  15  sq.  in.,  7  in. 

3.  16  sq.  in.,  9  in. 

4.  20  sq.  in.,  12  in. 


5.  18  sq.  in.,  25  in. 

6.  24  sq.  in.,  4  ft. 

7.  27  sq.  in.,  6  ft. 

8.  3  sq.  ft.,  21  in. 


9.  10  sq.ft.,  16  ft. 

10.  12  sq.  ft.,  18  ft. 

11.  15sq.  ft.,  20  ft. 

12.  18  sq.  ft.,  24  ft. 


Find  the  volume  of  a  square  prism,  the  side  of  the  base  and 
the  altitude  being,  respectively  : 


13.  10  in.,  12  in. 

14.  15  in.,  18  in. 

15.  16  in.,  24  in. 

16.  18  in.,  25  in. 


17.  2  ft.,  5  ft. 

18.  3  ft.,  42  in. 

19.  3  ft.,  45  in. 


21.  3  ft.  6  in.,  7  ft. 

22.  5  ft.  8  in.,  12  ft. 

23.  6  ft.  4  in.,  15  ft. 

24.  8  ft.  10  in.,  20  ft. 


20.  4  ft.,  6  ft. 

Find  the  volume  of  a  triangular  prism  whose  base  area,  and 
altitude,  respectively,  are  : 

25.  24  sq.  in.,  15  in.     29.   10  sq.  ft.,  12  ft.  33.  6  sq.  ft.,  3  ft.  6  in. 

26.  30  sq.  in.,  18  in.     30.   10  sq.  ft.,  15  ft.  34.  8  sq.  ft.,  2  ft.  9  in. 

27.  40  sq.  in.,  20  in.     31.   12  sq.  ft.,  12  ft.  35.  8  sq.  ft.,  3  ft.  8  in. 

28.  42  sq.  in.,  35  in.      32.  15  sq.  ft.,  10  ft.  36.  9  sq.  ft.,  5  ft.  3  in. 


MEASUREMENT  OF  SOLIDS 


235 


A  Circular  Cylinder  is  a  solid  bounded  by  a  uniformly  curved 
surface,  and  whose  ends  are  equal  circles  in  parallel  planes. 

A  circular  cylinder  is  formed  when  a  rectangle 
is  revolved  about  one  of  its  sides.  The  figure  at  the 
right  illustrates  the  formation  of  a  circular  cylinder 
by  revolution  of  a  rectangle. 

The  Altitude  of  a  Cylinder  is  the  perpendicular 
distance  between  the  bases. 

The  Lateral  Area  of  a  Cylinder  is  the  area  of  the 
curved  surface  of  the  cylinder. 

The  lateral  area  of  a  cylinder  is  illustrated  in  the  three  figures 
below. 


B 


£~ 


B 


If  the  rectangle  ABDC  is  rolled  up  until  the  edge  AB  falls  upon 
the  edge  CD  and  the  Unes  AC  and  ED  oi  the  given  rectangle  form 
equal  circles,  the  cyhnder  at  the  right  results.     In  general, 

The  lateral  area  of  a  cyhnder  is  equal  to  the  product  of  the  cir- 
cmnference  of  the  base  by  the  altitude. 

The  Total  Area  of  a  Cylinder  is 
the  sum  of  the  lateral  area  and  the 
area  of  the  two  bases. 

If  two  circles  P  and  K,  whose  cir- 
cumferences are  equal  respectively 
to  AB  and  CD,  are  folded  into  the 
cylinder,  the  total  area  of  the  sohd  is 
made  up  of  the  lateral  area  plus  the 
combined  area  of  the  two  circles. 


236  MEASUREMENT    OF   SOLIDS 

BLACKBOARD   PRACTICE 

Find  the  lateral  area  of  a  circular  cylinder  the  circumference  ot 
the  base  and  the  altitude  being,  respectively : 


1. 

15  in.,  10  in. 

5. 

2  ft.  3  in.,  10  in. 

9. 

3.1416  ft.,  4  ft. 

2. 

18  in.,  24  in. 

6. 

3  ft.  9  in.,  12  in. 

10. 

6.2832  ft.,  6  ft. 

3. 

20  in.,  30  in. 

7. 

4  ft.  6  in.,  18  in. 

11. 

5.1112  ft.,  5  ft. 

4. 

24  in.,  35  in. 

8. 

5  ft.  8  in.,  24  in. 

12. 

9.4248  ft.,  6  ft. 

Find  the  total  area  of  a  circular  cylinder  the  radius  of  the  base 
and  the  altitude  being,  respectively  : 

13.  6  in.,  15  in.         15.    10  in.,  25  in.  17.    1  ft.  3  in.,  5  ft. 

14.  8  in.,  18  in.         16.    12  in.,  30  in.  18.    2  ft.  6  in.,  6  ft. 

The  Volume  of  a  Circular  Cylinder  is  obtained  through  the  same 
principle  that  we  applied  in  finding  the  volume  of  a  prism.  A 
cyUnder  may  be  coi;isidered  as  a  prism  with  a  great  number  of  sides, 
these  sides  being  so  narrow  that  they  form  the  unbroken  curved 
surface  of  the  cylinder.  Considering,  therefore,  that  the  cylinder 
is  a  prism  with  a  very  great  number  of  sides,  we  may  find  its  volume 
in  the  same  way  that  we  would  find  the  volume  of  a  prism.     That  is, 

The  volume  of  a  circular  cylinder  is  equal  to  the  product  of  its 
altitude  and  the  area  of  its  base. 

BLACKBOARD   PRACTICE 

Find  the  volume  of  a  circular  cylinder,  if  the  area  of  the  base  and 
the  altitude  are,  respectively  : 

1.  10  sq.  in.,  15  in.  6.  2  sq.  ft.,  3  ft.  11.  1.5  sq.  ft.,  3  ft.  6  in. 

2.  12  sq.  in.,  18  in.  7.  2  sq.  ft.,  5  ft.  12.  2.4  sq.  ft.,  4  ft.  3  in. 

3.  15  sq.  in.,  20  in.  8.  3  sq.  ft.,  4  ft.  13.  3.1  sq.  ft.,  5  ft.  8  in. 

4.  16  sq.  in.,  20  in.  9.  4  sq.  ft.,  5  ft.  14.  4.5  sq.  ft.,  4  ft.  6  in. 
6.  18  sq.  in.,  24  in.  10.  5  sq.  ft.,  6  ft.  15.  5.6  sq.  ft.,  8  ft.  10  in. 


MEASUREMENT  OF  SOLIDS 


237 


Find  the  volume  of  a  circular  cylinder,  if  the  radius  of  the  base 
and  the  altitude  are,  respectively  : 


16.  4  in.,  10  in. 

17.  3  in.,  15  in. 

18.  5  in.,  12  in. 

19.  6  in.,  15  in. 

20.  9  in.,  18  in. 


21.  2  ft.,  3  ft.  6  in. 

22.  1ft.,  3  ft.  8  in. 

23.  2  ft., -1ft.  3  in. 

24.  1ft.  3  in.,  2  ft. 


26.  1ft.  3  in.,  3  ft.  6  in. 

27.  Ift.Gin.,  3  ft.  8in. 

28.  1ft.  9  in.,  4  ft.  6  in. 

29.  2  ft.  8  in.,  5  ft.  2  in. 

30.  3  ft.  6  in.,  6  ft.  10  in. 


25.   1ft.  Gin.,  5ft. 

A  Pyramid  is  a  solid  whose  base  is  a  regular  polygon  and  whose 
faces  are  triangles  that  meet  in  a  point. 


(a)  ^b) 

Pyramids  are  named  from  their  basos. 

(a)  is  a  triangular  pyramid.       (6)  is  a  rectangular  pyramid. 

(c)  is  a  hexagonal  pyramid. 

The  Vertex  of  a  Pjrramid  is  the  meeting-point  of  the  triangular 
faces. 

The  Altitude  of  a  Pyramid  is  the  perpendicular  distance  from  the 
vertex  to  the  base. 

The  Slant  Height  of  a  Pyramid  is  the  altitude  of 
any  one  of  the  equal  triangles  that  form  the  faces 
of  the  pyramid. 

In  the  figure  at  the  right 
The  vertex  is  A. 
The  altitude  is  AO. 
The  slant  height  is  AM. 


238 


MEASUREMENT   OF   SOLIDS 


The  Lateral  Area  of  a  Pyramid  is  the  combined  areas  of  the 
triangles  that  form  the  faces  of  the  pyramid. 

If  the  triangles  in 
(a)  at  the  right  are 
folded  on  AC,  AD, 
and  AE,  so  that 
A5  falls  on  A  5,  the 
lateral  area  of  a 
solid,  or  pyramid,  is 
formed  as  shown  in 
(6) .  The  area  of  any 
one  of  the  four  equal  faces,  as  ABC,  is  the  area  of  the  triangle 
ABC,  in  which  the  base  is  BC  and  the  altitude  AM.  That  is, 
area  of  triangle  ABC  =  ^{BC  X  AM).  Therefore,  the  area  of  all 
four  triangles  equals  one  half  the  product  of  the  sum  of  all  the 
bases  by  the  slant  height.    Or,  in  general, 

The  lateral  area  of  a  pyramid  equals  one  half  the  product  of 
the  slant  height  by  the  perimeter  of  the  base. 

The  Total  Area  of  a  Pyramid  is  the  sum  of  the  lateral  area  and 
the  area  of  the  base. 

BLACKBOARD   PRACTICE 

Find  the  lateral  area  of  a  pyramid  if  the  perimeter  of  the  base 
and  the  slant  height  are,  respectively : 

1.    15  in.,  10  in.        6.    2  ft.,  16  in. 


2. 

16  in.,  12  in. 

7. 

3. 

18  in.,  15  in. 

8. 

4. 

20  in.,  17  in. 

9. 

5. 

24  in.,  18  in. 

10. 

3  ft.,  24  in. 

4  ft.,  30  in. 
30  in.,  5  ft. 
36  in.,  6  ft. 


11.  2  ft.  6  in.,  3  ft.  6  in. 

12.  3  ft.  8  in.,  1  ft.  4  in. 

13.  4  ft.  4  in.,  2  ft.  10  in. 

14.  4  ft.  6  in.,  5  ft.  8  in. 

15.  5  ft.  3  in.,  6  ft.  8  in. 


Find  the  lateral  area  of  a  square  pyramid  when  the  length  of 
one  base  edge  and  the  slant  height  are,  respectively  : 


16.  8  in.,  15  in. 

17.  9  in.,  16  in. 


18.  9  in.,  20  in. 

19.  10  in.,  24  in. 


20.  12  in.,  36  in, 

21.  2  ft.,  5  ft. 


MEASUREMENT  OF  SOLIDS  239 

22.  2  ft.,  27  in.     25.    18  in.,  4  ft.  28.  2  ft.  6  in.,  3  ft.  8  in. 

23.  13  in.,  2ft.     26.   1  ft.  6  in.,  2  ft.  3  in.     29.  3  ft.  7  in.,  4  ft.  11  in. 

24.  14  in.,  5  ft.     27.   1  ft.  8  in.,  2  ft.  9  in.     30.  4  ft.  5  in.,  5  ft.  3  in. 

A  Cone  is  a  solid  whose  base  is  a  circle  and  whose  curved  sur- 
face tapers  uniformly  to  a  point. 

The  Vertex  of  a  Cone  is  the  point  to  which  the  curved  surface 
tapers. 

The  Altitude  of  a  Cone  is  the  perpendicular  distance  from  the 
vertex  to  the  base  of  the  cone. 

The  Slant  Height  of  a  Cone  is  the  distance  from  the  vertex  to  any 
point  on  the  circumference  of  the  base. 

In  the  figure  at  the  right  ^  * 

The  base  is  the  circle  whose  center  is  D. 

The  vertex  is  the  point  A. 

The  altitude  is  the  distance  AD. 

The  slant  height  is  the  distance  AB. 

The  radius  of  the  base  is  the  distance  DB. 

The  Lateral  Surface  of  a  Cone  is  the  curved  surface  between  the 
vertex  and  the  circumference  of  the  base. 

The  lateral  surface  of  a  cone  may  be  considered  as  made  up  of  a 
great  number  of  triangles,  the  altitude  of  each  triangle  being  the 
slant  height  of  the  cone,  and  the  sum  of  the  bases  of  all  the  triangles 
being  the  circumference  of  the  base.  Therefore,  the  lateral  area 
of  a  cone  may  be  found  by  use  of  the  principle  through  which  we 
found  the  lateral  surface  of  a  pyramid.     That  is. 

The  lateral  area  of  a  cone  is  equal  to  one  half  the  product  of  the 
slant  height  by  the  circumference  of  the  base. 

The  Total  Area  of  a  Cone  is  the  sum  of  the  lateral  area  and  the 
area  of  the  base. 


240 


MEASUREMENT   OF   SOLIDS 


1. 

8  in.,  6  in. 

6. 

2  ft.,  10  in 

2. 

8  in.,  7  in. 

7. 

2  ft.,  14  in 

3. 

9  in.,  5  in. 

8. 

2  ft.,  19  in 

4. 

9  in.,  6  in. 

9. 

18  in.,  2  ft 

5. 

10  in.,  8  in. 

10. 

19  in.,  3  ft 

BLACKBOARD   PRACTICE 

Find  the  lateral  area  of  a  cone  if  the  circumference  of  the  base 
and  the  slant  height  are,  respectively  : 

11.  2  ft.  4  in.,  2  ft.  6  in. 

12.  2  ft.  9  in.,  3  ft.  4  in. 

13.  3  ft.  6  in.,  4  ft.  8  in. 

14.  3  ft.  11  in.,  3  ft.  5  in. 

15.  4  ft.  10  in.,  5  ft.  11  in. 

Find  the  lateral  area  of  a  cone  if  the  radius  of  the  base  and  the 
slant  height,  respectively,  are  : 

26.  1  ft.  2  in.,  2  ft.  1  in. 

27.  1  ft.  7  in.,  3  ft.  4  in. 

28.  2  ft.  1  in.,  4  ft.  6  in. 

29.  3  ft.  5  in.,  5  ft.  5  in. 

30.  3  ft.  6  in.,  6  ft.  8  in. 

The  Volume  of  a  Pyramid  or  Cone. 

(1)  A  fixed  relation  exists  between  the  volume  of  a  prism  and 
the  volume  of  a  pyramid  having  the  same  base  and  altitude.     And, 

(2)  A  similar  relation  exists  between  the  volume  of  a  cylinder 
and  the  volume  of  a  cone  having  the  same  base  and  altitude. 


16. 

1  in.,  6  in. 

21. 

1  ft.,  21  in. 

17. 

2  in.,  6  in. 

22. 

1  ft.,  25  in. 

18. 

2  in.,  9  in. 

23. 

11  in.,  3  ft. 

19. 

3  in.,  15  in. 

24. 

15  in.,  2  ft. 

20. 

3  in.,  19  in. 

25. 

18  in.,  5  ft. 

H 


"^ 


UJ 
Q 


B  E  F 

(a) 


In  (a)  the  base  of  the  prism  equals  the  base  of  the  pyramid,  and 
the  altitude  of  the  prism  equals  the  altitude  of  the  pyramid. 

In  (b)  the  base  of  the  cylinder  equals  the  base  of  the  cone,  and 
the  altitude  of  the  cylinder  equals  the  altitude  of  the  cone. 


MEASUREMENT  OF  SOLIDS  241 

Then,  by  geometry : 

The  volume  of  the  pyramid  equals  one  third  the  volimie  of  the 
prism. 

And, 

The  volume  of  the  cone  equals  one  third  the  volume  of  the 
cylinder. 

A  simple  experiment  will  serve  to  establish  these  truths  in  a 
general  way,  and  will  illustrate  the  principle  without  proving  it. 
If  a  hollow  prism  has  the  same  base  as  a  hollow  pyramid,  and  if 
each  has  the  same  altitude,  the  amount  of  sand  that  just  fills  the 
prism  will  fill  the  pyramid  just  three  times.  That  is,  the  volume  of 
the  pyramid  is  one  third  the  volume  of  the  prism.  The  same 
practical  experiment  will  illustrate  the  fact  that  if  a  cylinder  and 
a  cone  have  the  same  base  and  altitude,  the  amount  of  sand  that 
exactly  fills  the  cylinder  will  fill  the  cone  three  times. 

BLACKBOARD   PRACTICE 

Find  the  volume  of  a  square  pyramid  if  the  edge  of  the  base  and 
the  altitude  are,  respectively  : 

1.  6  in.,  15  in.         4.    1  ft.,  2  ft.  7.    1  ft.  3  in.,  6  ft. 

2.  9  in.,  20  in.  5.    2  ft.,  8  ft.  8.    1  ft.  6  in.,  9  ft.  3  in. 

3.  9  in.,  28  in.  6.   30  in.,  9  ft.        9.    1  ft.  10  in.,  14  ft.  6  in. 

Find  the  volume  of  a  cone  if  the  diameter  of  the  base  and  the 
altitude  are,  respectively: 

10.  12  in.,  15  in.  16.  1  ft.  3  in.,  4  ft.  6  in. 

11.  16  in.,  20  in.  17.  1  ft.  6  in.,  5  ft.  8  in. 

12.  18  in.,  30  in.  18.  1  ft.  4  in.,  5  ft.  9  in.  1 

13.  2  ft.,  30  in.  19.  1  ft.  2  in.,  5  ft.  6  in. 

14.  3  ft.,  39  in.  20.  2  ft.  3  in.,  6  ft.  1  in. 

15.  27  in.,  4  ft.  21.  2  ft.  4  in.,  4  ft.  6  in. 


242 


MEASUREMENT   OF   SOLIDS 


(a) 


(b) 


(c) 


A  Sphere  is  a  solid  or  volume  bounded  by  a  surface  every  point 
of  which  is  equally  distant  from  a  point  within  called  the  center. 

(a)  illustrates  a  sphere. 

A  Diameter  of  a  Sphere  is  a  straight  line  passing  through  the 
center  of  the  sphere  and  terminating  in  its  surface. 

If  in  (b)  A  and  B  are  joined  by  a  straight  line,  AB  is  a  diameter. 
Similarly,  CD  would  be  a  diameter. 

A  Radius  of  a  Sphere  is  the  distance  from  the  center  to  any 
point  on  the  surface  of  the  sphere. 

All  diameters  pass  through  the  center  of  the  sphere.  Any  straight 
line  from  their  intersection  to  the  surface  of  the  sphere  is  a  radius  of  the 
sphere. 

A  Great  Circle  of  a  Sphere  is  a  circle  whose  plane  passes  through 
the  center  of  the  sphere,  and  whose  radius  equals  the  radius  of  the 
sphere. 

In  (6)  the  circles  through  A,  B,  C,  and  D  are  great  circles. 

The  Circumference  of  a  Sphere  is  the  circumference  of  a  great 
circle  of  the  sphere. 

The  circumference  of  a  sphere  is  the  greatest  distance  around  it. 

A  Hemisphere  is  one  of  the  two  sohds  into  which  a  sphere  is 
divided  by  a  great  circle. 

(c)  illustrates  two  hemispheres. 


MEASUREMENT  OF  SOLIDS  243 

The  Surface  of  a  Sphere.  In  later  mathe- 
matics it  is  proved  that  the  surface  of  a 
sphere  is  equal  to  the  area  of  four  great 
circles  of  that  sphere.     That  is, 

If  A  BCD  is  a  great  circle  of  the  sphere 
whose  radius  is  R,  the  surface  of  the  sphere 
equals  4  times  the  area  of  A  BCD,  or  ^tR^. 

A  simple  experiment  will  illustrate  the  princii)lo  without  proving 
it.  If  a  w^axed  cord  just  long  enough  to  cover  the  surface  of  the 
hemisphere  is  coiled  on  the  surface  of  the  great  circle  of  the  hemi- 
sphere, it  will  be  found  that  the  cord  covers  the  great  circle 
just  twice.  Hence,  the  area  of  the  surface  of  the  hemisphere  is 
equal  to  the  area  of  two  great  circles  of  that  hemisphere ;  and  it 
follows,  therefore,  that  the  area  of  the  whole  surface  of  the  sphere 
is  equal  to  the  area  of  four  great  circles  of  the  sphere. 


BLACKBOARD    PRACTICE 

Using  3.1416-  for  t,  find  the  surface  of  the  sphere  whose 


Radius  is : 

Diameter  is : 

1.    2  in. 

7. 

1ft. 

13. 

10  in. 

19. 

1ft. 

2  in. 

2.    3  in. 

8. 

1.1  ft. 

14. 

14  in. 

20. 

1ft. 

3  in. 

3.   4  in. 

9. 

1.5  ft. 

15. 

15  in. 

21. 

1  ft. 

4  in. 

4.    5  in. 

10. 

1.6  ft. 

16. 

18  in. 

22. 

1  ft. 

7  in. 

5.    0  in. 

11. 

1.8  ft. 

17. 

20  in. 

23. 

1ft. 

9  in. 

6.    8  in. 

12. 

1.25  ft. 

18. 

23  in. 

24. 

1  ft. 

10  in 

25.  How  many  square  feet  are  there  in  the  surface  of  a  hemi- 
spherical dome  whose  diameter  is  24  feet  ? 

26.  The  diameter  of  the  planet  Jupiter  is  1 1  times  the  diameter 
of  the  earth.  If  the  earth's  diameter  is  taken  as  8000  miles,  find 
the  number  of  square  miles  in  the  earth's  surface  and  the  number 
in  Jupiter's  surface. 


244  MEASUREMENT   OF   SOLIDS 

The  Volume  of  a  Sphere.  In  later  mathematics  it  is  proved  that 
the  volmne  of  a  sphere  is  equal  to  one  third  the  product  of  its  radius 
by  its  surface. 

The  principle  may  be  illustrated  by  the  accompanying  figure.     It  is 

evident  that  a  sphere  may  be  considered  as 
made  up  of  a  great  number  of  pjTamids,  each 
pjTamid  having  an  altitude  equal  to  the  radius 
of  the  sphere,  and  the  total  area  of  the  bases 
of  the  pjrramids  making  up  the  total  area  of 
the  sphere.  Therefore,  the  volume  of  a  sphere 
is  made  up  of  the  total  volume  of  all  the  pyra- 
mids, and  we  may  find  the  volume  of  the 
sphere  by  applying  the  rule  for  the  volume  of  a 
p\Tamid. 

The  vohime  of  a  pyramid  equals  one  third  the  product  of  the 
base  and  altitude. 

The  altitude  of  each  pyramid  is  the  radius  of  the  sphere. 

The  sum  of  the  bases  of  the  pyramids  is  the  surface  of  the  sphere. 
Therefore, 

Volume  of  a  Sphere  =  ^xR X ^ttR-  =  f ttR^ 


BLACKBOARD    PRACTICE 

Find  the  volume  of  a  sphere  whose 

Radius  is  :  Diameter  is  : 

1.  1  in.  6.  1  ft.  11.    5  in.  16.  1  ft.  3  in. 

2.  2  in.  7.  1.2  ft.  12.    8  in.  17.  1  ft.  4  in. 

3.  3  in.  8.  1.5  ft.  13.    9  in.  18.  1  ft.  8  in. 

4.  4  in.  9.  1.8  ft.  14.    11  in.  19.  2  ft.  3  in. 

5.  5  in.  10.  1.25  ft.  15.    13  in.  20.  2  ft.  6  in. 


PROMISSORY  NOTES  245 

PROMISSORY    NOTES 

A  Promissoiy  Note  is  a  written  promise  to  pay  a  sum  of  money 
on  demand  or  at  a  specified  time. 

A  promissory'  note  is  usually  called  a  Note. 

The  Maker  is  the  person  who  signs  the  note. 

The  Payee  Ls  the  person  to  whom  the  note  is  payable. 

The  Face  of  the  note  is  the  sum  whose  pajTnent  is  promised. 


..^'460.00                                               Jeekaen,   MlBtlislppi,   yebroarj  17,  /'^/9 

» three  Mentha  — « yija'A///nrA^/    I       ^/TYJmy.W  /rjia^u^y 

J^/A^ /^'t'r/^.r r'^  The  yield  4  StcTcna  Censtruotlcn  Ceopeny 

-—  Toxur  gandxed  Plfty ^C/ /^A? )A 

^l-.-^/uy/J^y/zi^     ?he  yirat  Setloaal   Bent  ef  JacicBon.  MlsalBBlppl. 


'^jaui&yrea:^!'^ 


In  the  note  illustrated 

The  maker  is  Chas.  Lansing. 

The  payee  is  The  Field  k.  Stevens  Construction  Company. 

The  face  of  the  note  is  S450. 

A  note  may  be  made  payable  in  three  ways. 
Ist  :  On  demand,  when  pa\Tnent  mav  be  asked  for  at  anv  time. 
2d  :    At  a  specified  time  after  date,  at  which  time  the  note  is  due. 
3d :    At  a  specified  date,  upon  which  date  it  is  due. 

The  Day  of  Maturity  is  the  date  at  which  a  note  specifying  tim^ 
is  due. 

The  day  of  maturity  in  the  above  note  is  the  date,  March  17, 
1919,  that  is,  the  date  at  the  end  of  the  time  specified  in  the  note. 

A  note  bears  interest  in  accordance  with  its  conditions. 

(1)  If  written,  ''  with  interest,"  and  with  the  rate  indicated,  a 
note  bears  interest  at  that  rate  for  the  time  reckoned  from  the  date 
of  the  note  to  the  dav  of  maturitv. 


246 


PROMISSORY   NOTES 


(2)  If  written,  "  with  interest,"  but  without  indicating  a  rate, 
a  note  bears  interest  from  the  date  of  the  note  to  the  day  of 
maturity  with  interest  at  the  legal  rate  in  the  state  in  which  it  is 
payable.  * 

(3)  If  no  mention  of  interest  is  written  in  the  note,  no  interest 
can  be  collected  for  the  time  between  the  date  of  the  note  and  the 
day  of  maturity  ;  but  if  the  note  is  not  paid  at  maturity,  it  begins 
to  draw  interest  from  that  date  at  the  legal  rate. 

A  Negotiable  Note  is  a  note  made  paj^able  to  the  payee,  or  order. 

By  Indorsement  a  negotiable  note  may  be  made  payable  to 
another  person. 

Illustration : 

John  Nicholson  gives  his  note  to  John  Anderson. 

The  illustrations  show  three  common  forms  of  indorsement. 


-yt?A!^>^-'^U^-«^e/t^<»»^^ 


The  payee,  John  Anderson,  can  make  the  note  payable  to  any 
other  person  who  may  subsequently  hold  it  by  writing  his  name 
on  the  back  as  illustrated  at  the  left. 

#  This  is  called  Indorsement  in  Blank,  and  it  indicates  that  Mr. 
Anderson  has  actually  sold  the  note  and  indicates  by  his  indorse- 
ment that  he  has  received  value  for  it. 

If  the  payee  should  sell  the  note  to  W.  A.  Rogers,  and  should 
prefer  to  guard  against  the  possible  loss  and  the  presentation  by 
some  other  person,  he  indorses  it  with  the  words,  ''  Pay  to  the 
order  of  W.  A.  Rogers,"  and  then  signs  his  own  name.  This  is 
called  an  Indorsement  in  Full. 


PROMISvSORY  NOTES  247 

If  Ml .  Anderson  wishes  to  release  himself  from  any  future  re- 
sponsibility for  the  payment  of  the  note,  he  may  write  the  words, 
'"  without  recourse,"  over  his  signature. 

This  is  called  a  Qualified  Indorsement. 

A  Non-negotiable  Note  is  a  note  written  without  the  words,  "  or 
order,"  and  is  payable  only  to  the  payee. 

WRITTEN   APPLICATIONS 

Supplying  names  for  the  maker  and  the  psivee,  write  negotiable 
notes  for  each  of  the  following  conditions  : 

1.  Face  $200;  date  April  17,  1919;   tune  4  mo. ;   rate  6%. 

2.  Face  $500 ;   date  January  10,  1919  ;   time  6  mo. ;  rate  6%. 

3.  Face  $750;  dated  Dec.  20,  1918  ;  time  9  mo. ;  rate  5%. 

4.  Face  $1000 ;  date  May  9,  1919  ;  tune  60  da. ;  rate  6%. 

5.  Face  $2500  ;  date  October  10,  1919  ;  time  90  da. ;  rate  5^%. 

6.  Face  $4000;  date  July  5,  1918 ;  tune  30  da. ;  rate  5%. 

7.  Indorse  three  of  the  above  notes  in  blank,  and  the  other 
three  in  full. 

8.  Write  a  non-negotiable  note,  without  interest,  with  your- 
self as  payee  and  Frederick  Thompson  as  maker,  the  face  to  be 
$150,  the  date  January  10,  1919,  and  the  time  60  days. 

9.  Write  a  demand  note  for  one  hundred  dollars  payable  to 
yourself,  the  maker  being  Franklin  Spencer,  and  the  note  to  bear 
interest  at  5%. 

10.  Write  a  90-day  note  for  two  hundred  dollars,  payable  to 
Edward  Rutledge  and  made  bv  vourself .  Put  three  different 
indorsements  on  it. 


248  PROIMISSORY  NOTES 

PARTIAL   PAYMENTS 

The  maker  of  a  note  is  often  able  to  pay  a  part  of  the  face  be- 
fore the  whole  is  due. 

Payments  made  upon  a  note  during  the  time  it  runs  are  called 
Partial  Pa3mients. 

When  partial  payments  are  made  the  amount 
paid  is  written  upon  the  back  of  the  note, 
together  with  the  date  of  the  payment.  An 
indorsement  of  this  kind  is  a  legal  receipt. 
The  illustration  at  the  right  shows  the  manner 
of  indorsing  three  different  partial  payments 
made  on  a  9-months  note  for  $1000. 

The  United  States  Rtile 

The  United  States  Rule  is  the  most  widely  used  rule  for  partial 
payments. 

It  has  been  decided  by  the  Supreme  Court  of  the  United  States 
that  in  the  settlement  of  a  note  on  which  one  or  more  partial  pay- 
ments have  been  made,  no  interest  may  be  allowed  on  a  payment, 
or  on  interest  due  on  the  note.  Hence,  the  United  States  Rule  is 
based  upon  the  following  principles  : 

(1)  Any  payment  must  be  applied  to  the  paying  of  interest  due. 

(2)  If  any  payment  exceeds  the  interest  due,  the  balance  of  that  pay- 
ment  must  reduce  the  principal. 

(3)  Interest  must  not  be  charged  upan  interest. 

Illustration : 

A  note  for  one  thousand  dollars  is  dated  January  10,  1919,  and 
bears  interest  at  6%.  The  following  payments  are  indoreed : 
March  1,  1919,  $200;  May  10,  1919,  $300;  July  12,  1919,  $200. 
Settlement  is  made  on  August  5,  1919.  Find  the  balance  due  on 
that  date. 


PROMISSORY  NOTES  249 

Principal,  January  10,  1919 $1000.00 

Interest  to  date  of  1st  payment 

January  10,  1919  to  March  1,  1919  :   1  mo.  21  da.  8.50 

Amount  due $1008.50 

First  payment 200.00 

New  Principal,  March  1,  1919 $808.50 

Interest  to  date  of  2d  payment 

March  1,  1919  to  May  10,  1919  :  2  mo.  10  da.    .  9.4:3 

Amount  due $817.93 

Second  payment 300.00 

New  Principal,  May  10,  1919 $517.93 

Interest  to  date  of  3d  payment 

May  10,  1919  to  July  12,  1919  :  2  mo.  2  da.    .     .  5.35 

Amount  due $523.28 

Third  payment 200.00 

New  Principal,  July  12,  1919 $323.28 

Interest  to  date  of  settlement 

July  12,  1919  to  August  5,  1919 :  24  da.     .     .     .  1.30 

Amount  due  at  settlement $324.58      Result. 

The  process  in  the  illustration  follows  the 

Rule :  Find  the  amount  of  the  principal  to  the  date  of  the  first 
payment. 

Subtract  the  first  payment  from  this  amount. 

With  the  remainder  as  a  New  Principal  repeat  the  process,  finding 
the  arnount  of  the  new  principal  to  the  date  of  the  second  payment. 

Subtract  the  second  payment  and  proceed  as  before. 

If,  at  any  time,  a  payment  does  not  equal  or  exceed  the  interest  due, 
find  the  interest  to  the  time  when  two  or  more  payments  equal  or  exceed 
the  interest. 

The  use  of  the  method  when  interest  due  exceeds  a  payment  is 
illustrated  in  the  following  example.  It  wall  be  observed  that  a 
payment  of  $50  is  made  at  a  date  when  the  interest  due  exceeds 
that  payment.     Note  w^hat  is  done  in  this  case. 


250  PROMISSORY   NOTES 

A  promissory  note  is  dated  June  1,  1917,  and  is  to  run  2  years. 
The  face  of  the  note  is  $2000,  the  rate  6%,  and  the  indorsements 
are:  January  16,  1918,  $100;  July  16,  1918,  $50;  January  1,  1919, 
$500.     What  was  due  at  maturity? 

Principal,  June  1,  1917 $2000.00 

Interest  to  date  of  1st  payment 

June  1,  1917  to  January  16,  1918 :  7  mo.  15  da.  75.00 

Amount  due $2075.00 

First  payment        100.00 

New  Principal,  January  16,  1918 $1975.00 

Interest  to  date  of  2d  payment 

January  16,  1918  to  July  16,  1918  :  6  mo.       .     .  59.25 

Second  payment,  less  than  interest  due,  $50.00  .     . 
Interest  on  $1975.00 

July  16,  1918  to  January  1,  1919 :  5  mo.  15  da.  54.31 

Amount  due $2088.56 

Third  payment.  $500  +  second  payment,  $50     .     .         550.00 

New  Principal,  January  1,  1919 $1538.56 

Interest  to  date  of  settlement 
•     January  1,  1919  to  June  1,  1919 :  6  mo.      .     .     .  46.16 

Amount  due  at  settlement $1584.72      Result. 

The  student  will  observe  and  remember  that 

The  United  States  Rule  applies  partial  payments  first  to  pay 
interest  due;  and  second,  if  any  part  of  the  payment  is  left,  to  reduce 
the  principal. 

WRITTEN   APPLICATIONS 

1.  A  note  for  $500  is  dated  Jan.  1,  1916,  and  bears  interest 
at  6%.  An  indorsement  of  $200  was  made  March  15,  1916.  What 
amount  was  due  at  settlement,  Sept.  1,  1916  ? 

2.  A  note  for  $250.60  is  dated  July  7,  1917,  and  bears  interest 
at  7%.  Indorsements  are  as  follows:  September  20,  1917,  $80; 
January  1,  1918,  $50;  March  13,  1918,  $50.  What  amount  was 
due  at  settlement,  April  15,  1918? 


PROMISSORY  NOTES  251 

3.  A  note  for  $800  is  dated  June  4,  1917,  and  bears  interest  at 
6%.  Indorsements  are  :  May  1,  1918,  $144  ;  October  1, 1918,  $90 ; 
January  1,  1919,  $400 ;  and  February  4,  1919,  $100.  What  amount 
was  due  January  1,  1920? 

4.  A  note  for  $6255  is  dated  October  1,  1917,  and  bears  interest 
at  6%.  The  indorsements  are :  January  1,  1918,  $2000 ;  Novem- 
ber 1,  1918,  $200;  and  January  1,  1919,  $3000.  What  amount 
was  due  when  the  settlement  is  made  on  May  1,  1919? 

5.  A  note  for  $750  bears  interest  at  6%,  is  dated  April  7,  1916, 
and  has  the  following  indorsements:  January  17,  1917,  $200; 
March  13,  1918,  $25;  February  19,  1919,  $30;  August  3,  1919, 
$200 ;  January  1,  1920,  $150.  What  amount  was  due  on  the  note 
at  settlement  on  August  14,  1920  ? 

6.  On  a  note  for  $1000  bearing  interest  at  6%  there  are  made 
four  payments  of  $100,  $200,  $300,  and  $400,  on  the  dates,  April  1, 
July  1,  October  1,  and  January  1,  1914,  respectively.  The  date 
of  the  note  was  January  1,  1913.  What  amount  was  due  at  settle- 
ment on  January  1,  1918? 

The  Mercantile  Rule 

The  Mercantile  Rule  is  used  by  bankers  and  by  business  men 
on  short-time  notes,  that  is,  notes  that  are  to  run  only  a  few  months. 
The  rule  is  based  upon  two  principles  : 

(1)  The  face  of  the  note  shall  draw  interest  for  the  entire  time  that 
the  note  runs. 

(2)  Each  payment  shall  draw  interest  from  its  date  to  the  date  of 
settlement. 

By  this  rule,  therefore,  the  maker  of  the  note  is  credited  with 
interest  on  any  partial  payment  for  the  tune  he  advances  it  on  the 
note. 

The  amount  due  at  settlement  is  the  difference  between  the 
amount  of  the  face  at  that  date  and  the  total  amounts  of  payments 
and  interest  thereon  during  the  time  the  note  runs. 


254 


LONGITUDE   AND   TIME 


DiflEerence  in  Longitude  of  Two  Given  Places 

In  finding  the  number  of  degrees  of  circular  measure  between  two 
given  points  we  must  consider  the  location  of  each  relative  to  the 
prime  meridian.     There  are  two  possible  cases. 

1.  When  the  two  places  considered  are  both  east  of,  or  both 
^est  of,  the  prime  meridian. 

2.  When  the  two  places  are  on  opposite  sides  of  the  prime 
meridian. 


In  the  figure  (1) 

Longitude  of  A  =45°  W. 
Longitude  of  B  =30°  W. 

Hence,  the  difference  in  their  lo- 
cation, expressed  in  degrees,  is 
45° -30°  =  15°. 

Therefore, 

Difference  in  Longitude  is  15°. 

If  both  A  and  B  were  east  of  the 
prime  meridian,  the  difference  in 
their  longitude  would  be  obtained 
by  subtraction. 

If  A  were  north  of  the  equator 
and  B  were  south  of  it,  the  differ- 
ence in  their  longitude  would  be  the 
same,  15°. 


In  the  figure  (2) 

Longitude  of  M  =45°  W. 
Longitude  of  Ar=60°  E. 

Hence,  the  difference  in  their  lo- 
cation, expressed  in  degrees,  is 
45°  4-60°  =  105°. 

Therefore, 

Difference  in  Longitude  is  105°. 

In  this  case,  the  measurement  is 
made  up  of  two  different  portions, 
both  measured  from  the  same  point 
but  in  opposite  directions. 

Here,  as  in  the  first  case,  we  are 
seeking  to  find  the  number  of  de- 
grees of  measurement  between  the 
two  points. 


LONGITUDE  AND  TIME  255 

From  these  illustrations  we  have  the  general  rule : 

When  two  places  are  both  in  east  longitude,  or  both  in  west 
longitude,  the  difference  in  their  longitudes  is  found  by  sub- 
traction. 

When  one  place  is  east,  and  the  other  is  west,  longitude,  the 
difference  in  their  longitudes  is  found  by  addition. 

BLACKBOARD    PRACTICE 

Find  the  difference  in  longitude  between  two  places  whose 
longitudes  are  respectively : 

1.  30°E.,45°E.           7.   30°E.,  45°W.  13.  0°,  57°  W. 

2.  20°  E.,  75°  E.           8.   30°  W.,  60°  E.  14.  45°  E.,  90°  E. 

3.  45°W.,  75°W.         9.   45°  W.,  45°  E.  15.  60°  W.,  35°  E. 

4.  10°W.,  90°W.  10.   60°E.,30°W.  16.  16°  E.,  96°  W. 
6.  5°E.,  120°E.  11.    100°E.,  50°W.  17.  35°  W.,  80°  W. 
6.  15°W.,  135°W.  12.   90°W.,77°E.  18.  81°  W.,  37°  E. 

19.  10°  30'  E.,  25°  15'  E.  22.    15°  20'  W.,  85°  45'  W. 

20.  15°  30'  E.,  70°  20'  E.  23.   45°  10'  W.,  98°  25'  W. 

21.  90°  10'  W.,  75°  10'  W.  24.    60°  45'  E.,  10°  17'  W. 

25.  What  is  the  difference  in  longitude  of  Boston,  71°  3'  50"  W., 
and  Denver,  104°  58'  0"  W.  ? 

26.  What  is  th'e  difference  in  longitude  of  San  Francisco,  122° 
25'  42"  W.,  and  Chicago,  87°  36'  45"  W.? 


ro  Of  alt 


27.  What  is  the  difference  in  longitude  of  Washington,  77°  3'  6 
W.,  and  Pittsburg,  80°  2'  0"  W\? 

28.  W^hat  is  the  difference  in  longitude  of  London,  0°  5'  48"  W., 
and  New  York,  74°  0'  24"  W\? 


256  LONGITUDE   AND   TIME 

The  Relartion  between  Longitude  and  Time 

Once  Every  Twenty-four  Hours  a  complete  revolution  through  a 
circumference  of  360°  is  made  by  every  point  between  the  poles 
on  the  earth's  surface.     Therefore, 

In  1  hour  any  point  passes  through  — —,  or  through  15°  of  longi- 
tude. 
Again,  since  1  minute  of  time  equals  ^  of  1  hour, 

In  1  ndnute  any  point  passes  through  -|^°,  or  ^°,  or  15'  of  longitude. 
Finally,  since  1  second  of  time  equals  -J^  of  1  minute, 

In  1  second  any  point  passes  through  if',  or  -J',  or  15''  of  longitude. 
These  corresponding  equivalents  should  he  memorized. 

Table  of  Relation  between  Longitude  and  Time 


j 

360° 

of  longitude  correspond  to  24  hours  of  time 

15° 

of  longitude  correspond  to  1  hour  of  time 

15' 

of  longitude  correspond  to  1  minute  of  time 

15" 

of  longitude  correspond  to  1  second  of  time 

It  is  helpful  to  remember,  also,  that 

(1)  When  the  sun's  rays  are  vertical  on  any  point  on  a  meridian, 
it  is  noon  at  all  places  on  that  meridian. 

(2)  The  earth  turns  from  west  to  east,  hence  it  appears  that  the 
sun  moves  from  east  to  west. 

(3)  When  it  is  noon  at  any  place  it  is  before  noon,  or  earher,  at 
all  points  west  of  that  place,  for  the  sun  has  not  yet  become  ver- 
tically located  over  the  meridians  of  those  places. 

(4)  When  it  is  noon  at  any  place  it  is  after  noon,  or  later,  at  all 
points  east  of  that  place,  for  the  sun  has  already  been  vertically 
located  over  the  meridians  of  those  places. 

The  navigator  of  a  ship  sometimes  uses  the  difference  in  time 
between  two  places  to  determine  his  longitude ;  and,  if  he  knows 
the  difference  in  longitude,  to  determine  the  time. 


LONGITUDE  AND  TIME 


25; 


I.   To  Find  the  Difference  in  Time  between  Two  Places,  When 
the  Difference  in  the  Longitude  of  the  Places  Is  Known. 

Illustration : 

When  it  is  noon  at  Denver  (104°  58'  C'  W.)  what  time  is  it  at 
Boston  (71°  3'  50"  W.)  ? 

The  difference  in  longitude  is  33°  54'  10".  We 
have  found  that  15°  corresponds  to  1  hr.,  15'  to 
1  inin.,  and  15"  to  1  sec.  Therefore,  the  differ- 
ence in  time  between  the  two  given  places  is  as 
many  lionrs,  minutes,  and  seconds,  respectively, 
as  there  are  degrees,  minutes,  and  seconds  in  one  fifteenth  of  the  differ- 
ence in  longitude.  In  this  particular  illustration  Boston  is  east  of  the 
point  where  the  time  is  noon ;  hence  it  is  later  than  noon  in  Boston  by  the 
time  obtained,  that  is,  2  In*.  15  min.  36|  sec.  That  is,  when  it  is  noon  at 
Denver  it  is  15  minutes  and  37  seconds  after  2  o'clock  in  Boston.  (The 
time  is  to  the  nearest  second.) 

Longitude  of  Jmportant  Cities 


104° 
71° 

58' 
3' 

0" 
50" 

5)  33° 

54' 

10" 

2 

15 

36| 

Boston     .     . 

.       7F  03'  50"  W. 

Bombay    . 

72°  45'  56"  E. 

Chicago   .     . 

87°  36'  45"  W. 

Canton 

113°  16'  30"  E. 

Denver    .     . 

104°  .58'  00"  W. 

Cape  Town 

18°  28'  40"  E. 

New  York    . 

74°  00'  24"  W. 

London     . 

0°  05'  48"  W. 

Pittsburgh    . 

.       80°  02'  00"  W. 

Manila 

120°  58'  06"  E. 

Portland,  Me. 

70°  15'  40"  W. 

Melbourne 

'   144°  58' 35"  E. 

San  Francisco   . 

122°  25'  42"  W. 

Paris     . 

2°  20'  14"  E. 

Washington 

77°  03'  06"  W. 

Tokyo 

139°  44'  30"  E. 

BLACKBOARD    PRACTICE 


•Using  the  longitudes  given  in  the  table  find  the  difference  in  time 
between : 


1.  Boston  and  Pittsburgh. 

2.  New  York  and  London. 

3.  Portland  and  Pittsburgh. 


4.  New  York  and  Chicago. 

5.  Washington  and  Denver. 

6.  New  York  and  San  Francisco. 


258 


LONGITUDE   AND   TIME 


7.  Chicago  and  San  Francisco. 

8.  New  York  and  Paris. 

9.  Canton  and  London. 

10.  Tokyo  and  Paris. 

11.  Boston  and  Denver. 

12.  Denver  and  New  York. 

13.  Pittsburgh  and  Denver. 

14.  Boston  and  Chicago. 


15.  Cape  Town  and  Melbourne. 

16.  Canton  and  Bombay. 

17.  Canton  and  Tokyo. 

18.  London  and  Paris. 

19.  New  York  and  Manila. 

20.  London  and  Denver. 

21.  Paris  and  San  Francisco. 

22.  Melbourne  and  New  York. 


When  the  sun's  rays  are  vertical  upon  the  meridian  at  Washing- 
ton, find  the  time  at  each  of  the  following  places  : 


23.  Chicago. 

24.  Denver. 

25.  Pittsburgh. 


26.  Boston. 

27.  Manila.        ' 

28.  San  Francisco. 


29.  London. 

30.  Tokyo. 

31.  Canton. 


n.   To  Find  the   Difiference  in*the  Longitude  of  Two  Places, 
When  the  Difference  in  the  Time  of  the  Places  Is  Known. 

Illustration : 

1.  The  difference  in  the  time  at  New  York  and  at  Denver  is  2  hr. 
3  min.  50.4  sec.      What  is  the  difference  in  the  longitude  of  the 


We  have  found  that  1  hour  of  time 
corresponds  to  15°  of  longitude,  and  that 
1  minute  of  time  corresponds  to  15'  of 
longitude,  and  that  1  second  of  time 
corresponds  to  15"  of  longitude.  Theue- 
fore,  the  difference  in  the  longitude  is  as 
many  degrees  as  15  times  the  number 
of  hours,  as  many  minutes  as  15  times  the  number  of  minutes,  and  as 
many  seconds  as  15  times  the  number  of  seconds.  That  is,  the  difference 
in  longitude  of  New  York  and  Denver  is  15  times  (2  hr.  3  min.  50.4  sec), 
or  30°  57'  36". 


two  cities? 

hr. 

mm. 

sec. 

2 
30 

3 
57 

50.4 
15 
36 

30° 

57' 

36" 

the 
in 

difference 
longitude. 

LONGITUDE  AND  TIME  259 

2.    Find  the  longitude  of  Paris,  its   time   being   o   hours,  5 
minutes,  22.5  seconds  earher  than  New  York. 


hr. 

min. 

sec. 

5 

22 

22.5 

76°     20' 

38"  dif.  in  longitude 

15 

74°     00' 

24"  W.  (New  York) 

76 

20 

38 

2°     20' 

14"  E.,   the  longitude  of 

76° 

20' 

38'' 

the  difference 

Paris. 

in  longitude 

Since   1 

hr.   corresponds  to   15°,    1 

min.  to  15',  and  1  sec.  to  15",  the 
difference  in  longitude  between  Paris  and  New  York  is  as  many  degrees, 
minutes,  and  seconds,  respectively,  as  there  are  hours,  minutes,  and 
seconds  in  15  times  the  difference  in  time  between  the  two  places.  This 
difference  in  longitude  we  find  to  be  76°  20'  38" ;  and  as  this  difference  is 
greater  than  the  longitude  of  New  York  (74°  00'  24")  by  2°  20'  14", 
Berlin  must  be  east  of  the  prime  meridian  by  that  longitude. 

BLACKBOARD    PRACTICE 

Find  the  longitude  of  the  place  whose  time,  when  the  sun  is  on 
'.he  meridian  at  Washington,  D.  C,  is 


1. 

2.00  P.M. 

7. 

10.00  A.M. 

13. 

3.15i  P.M. 

2. 

3.00  P.M. 

8. 

9.15  A.M. 

14. 

1.20f  P.M. 

3. 

4.30  P.M. 

9. 

7.30  A.M. 

15. 

O.lOi  A.M. 

4. 

6.45  P.M. 

10. 

5.50  A.M. 

16. 

10.15iP.M. 

5. 

8.30  P.M. 

11. 

6.20  a.m: 

17. 

11.15|  P.M. 

6. 

11.00  P.M. 

12. 

4.00  A.M. 

18. 

12.20i  A.M. 

19.  The  Stock  Exchange  at  Paris  closes  at  3  p.m  on  their  merid- 
ian. What  is  the  corresponding  time  in  New  York?  the  dif- 
ference in  longitude? 

20.  An  accident  occurred  in  Rome  at  4  hr.  45  min.  49y3^  sec. 
A.M.  Monday.  What  is  the  longitude  of  Rome  if  the  corresponding 
time  in  New  York  was  11  p.m.  Sunday? 


260 


MEASUREMENT   OF   PUBLIC   LANDS 


Base  L 


B 


/ne 


■I 


a 


^ 


MEASUREMENT   OF   PUBLIC   LANDS 

The  public  lands  in  the  Western  and  the  Southern  states  have 
been  systematically  divided  into  townships  and  sections. 

A  Township  is  a  square  whose  sides  are 
6  miles  long.  A  township  contains  36 
square  miles.  The  sides  of  a  township 
run  east  and  west,  and  north  and  south. 

A  Section  is  one  of  the  square  miles 
into  which  a  township  is  divided. 

A  section  of  1  square  mile  contains, 
therefore,  640  acres.  a  Tract 

Tracts  are  laid  out  as  in  the  figure  above.    An  east  and  west  line  is 
chosen  for  a  base  line,  and  a  north  and  south  line  for  a  principal  meridian. 

Lines  parallel  to  the  base  line,  with  other 
lines  parallel  to  the  principal  meridian,  cut 
the  tract  into  square  townships. 

Townships  run  east  and  west  in  iiers^  and 
north  and  south  in  ranges.  Thus:  The 
township  B  in  the  figure  is  in  the  second  tier 
north  and  in  the  fourth  range  west.  Hence, 
B  is  numbered  "  T.  2  N.,  R.  4  W."  The  sec- 
tions in  a  township  are  numbered  as  in  the 
figure.  The  drawing  at  the  left  represents 
the  division  of  the  township  B  above  into  36 
.  ^       , .  "  sections  "  of  one  square  mile  each. 

A  Township 

Each  section  is  then  divided  into  parts, 
and  the  drawing  at  the  right  represents 
section  10  from  the  township  plan.  Ex- 
cepting its  shaded  part,  each  portion  of 
the  section  is  namecj.  The  shaded  portion 
with  reference  to 

(1)  Its  location  in  the  section  ; 

(2)  Its  township ;  and 

(3)  Its  tract ; 
is  called  S.  W.  i  of  N.  E.  i,  Sec.  10,  T.  2  N.,  R.  4  W. 


6 
7 
18 
19 
30 
31 

5 

8 
17 
20 
29 
32 

4 

3 
10 
15 
22 

27 
34 

2 
11 
14 

1 
12 
13 
24 
25 
36 

9 
10 
21 
28 
33 

23 
26 
35 

N.W.i 


S.4 


MEASUREMENT   OF   PUBLIC   LANDS 


261 


ORAL   PRACTICE 

If  each  of  the  drawings  represents  Section  10  of  the  Township  B, 
give  the  location  of  each  of  the  shaded  portions. 


■      I 


1.  How  many  acres  are  there  in  the  shaded  part  of  (a)  ? 

2.  How  many  acres  are  there  in  the  shaded  part  of  (b)  ? 

3.  How  many  acres  are  there  in  the  shaded  part  of  (c)  ? 

4.  How  many  acres  in  each  of  the  shaded  parts  of  (d)  ? 

Give  the  location  of  each  of  the  shaded  portions  in  the  following. 
Thus :  The  shaded  part  of  No.  1  is  the  ''  S.  W.  \  of  N.  E.  \  of 
Sec.  10  T.  2  N.,  R.  4. 


>j 


'  V 

'X  '  .^  ' 

f-' 

J 

—.MJiiiiiiTfhi 

(I) 


I-.' 


(4) 


WRITTEN   PRACTICE 

Draw  a  plan  containing  townships  as  in  a  tract 
Show  the  following  in  your  plan  : 

1.  T.  3  N.,  R.  2  W. 

2.  T.  3  N.,  R.  3  W. 

3.  T.  4  N.,  R.  2  E. 

On  the  plan  of  a  township  locate  : 

7.   Section  12.  8.   Section  23 

On  the  plan  of  a  section  indicate  : 


4.  T.  1  N.,  R.  4  AV. 

5.  T.  3  N.,  R.  2  W. 

6.  T.  2  N.,  R.  3  E. 


9.   Section  25. 


10.  S.  I-  of  N.  E.  \, 

11.  S.  E.  i  of  N.  W.  \. 


12. 
13. 


S.  W 

S.  E. 


\  of  N.  E.  \. 


4  of  N.  W. 


1 


262 


METRIC    SYSTEM 


THE   METRIC   SYSTEM 

The  Metric  System  is  a  decimal  system  of  weights  and  measures. 
The  Meter  is  the  principal  unit  of  the  metric  system. 

The  meter  was  origing/ted  by  the  French  government  and  was  intended 
to  be  a  length  exactly  one  ten-milHonth  part  of  the  distance  from  the 
equator  to  either  pole  of  the  earth's  surface.  Due  to  a  slight  error,  how- 
ever, the  meter  is  not  exactly  the  length  intended,  but  the  usefulness  of 
this  system  is  in  no  way  impaired  by  that  error. 

Principles  Underlying  the  Metric  System 

The  standard  unit  of  the  system  is  the  meter. 

Units  smaller  than  this  standard  are  made  by  dividing  the  meter 
decimally. 

Still  smaller  units  are  made  by  further  decimal  divisions. 

The  successive  decimal  divisions  are  named  by  using  Latin  or 
Greek  prefixes.     Thus : 

deci   means  .1  Hence,  decimeter   means  .1  of  a  meter 

centi  means  .01  Hence,  centimeter  means  .01  of  a  meter 

miUi  means  .001  Hence,  milLimeter  means  .001  of  a  meter 

Units  larger  than  the  standard  are  made  by  multiplying  the 
standard  unit  by  10  or  by  multiples  of  10.     Thus  : 

deka   means  10  times  Hence,  dekameter   means  10  meters 

hekto  means  100  times  Hence,  hektometer  means  100  meters 

kilo     means  1000  times  Hence,  kilometer     means  1000  meters 

The  three  subdivisions  of  the  standard  unit,  together  with  tlie 
three  multiples  of  that  unit,  make  up  the  table  for 

Metric  Measures  of  Length 


10  milUmeters  (mm.)  =  1  centimeter 

abbreviated  cm. 

10  centimeters             =  1  decimeter 

"           dm. 

10  decimeters              =  1  meter 

"           m. 

10  meters                     =  1  dekameter 

"           Dm. 

10  dekameters             =  1  hektometer 

Km. 

10  hektometers           =  1  kilometer 

Km. 

METRIC  SYSTEM 


263 


Convenient    approximate    equivalents    in    terms    of    English 
Standards. 


1  meter        =39.37  inches 
1  kilometer  =  .6214  mile 


1  yard  =  .9144  meter 
1  mile  =  1.609  kilometers 


The  meter  is  used  in  measuring  short  distances,  fabrics,  etc. 

The  kilometer  is  used  in  measuring  long  distances  just  as  we  use 
the  mile. 

The  centimeter  and  the  milUmeter  are  in  common  use  in  the 
sciences. 

I  DECIMETER   (j\  METER) 


10  CENTIMETERS 

11  1 

1      1 

Mill 

Mini 

lll|i|l 

III  1 

1 

II  1 

III 

WO  MILLIMETERS 


Changing  from  One  Denomination  to  Another  Denomination. 
Since  each  denomination  in  the  table  is  ten  times  the  preceding 
denomination,  we  may  change  from  one  denomination  to  the  next 
higher  denomination  by  moving  the  decimal  point  07ie  place  to  the 
left. 


Thus  :     4500  mm.  =450  cm. 
450  cm.  =45  dm. 
45  dm.  =4.5  m. 


Also  :  1256  m.  =  125.6  Dm. 

125.6  Dm.  =12.56  Hm. 
12.56  Hm.  =  1.256  Km. 


The  same  principle  permits  us  to  change  from  one  denomination 
to  the  next  lower  denomination  by  moving  the  decimal  point  one 
place  to  the  right. 


Thus:  8  m.  =80  dm. 

15  cm.  =150  mm. 


Also  :     154.75  Km.  =  1547.5  Hm. 
24.135  Dm.  =241.25  M. 


For  a  general  illustration  it  is  helpful  to  note  that  1235672  mm.  = 
123567.2  cm.  =  12356.72  dm.  =  1235.672  m.  =  123.5672  Dm.  =  12.35672  Hm. 


264  METRIC   SYSTEM 

Advantage  of  the  Metric  System.     Compare  the  work  neces- 
sary in  the  following  transformations. 

(1)  The  EngHsh  System,  by  long  and  careful  calculation,  shows  that 

4.352  mi.  =  1392.64  rd.  =7659.52  yd.  =22978.56  ft. 

(2)  The  Metric  System,  hy  merely  moving  the  decimal  'point,  shows  that 

4.352  Km.  =43.52  Hm.  =435.2  Dm.  =4352  m. 

In  changes  to  higher  denominations  the  advantage  in  the  metric 
system  is  even  greater. 

BLACKBOARD    PRACTICE 

Change  to  meters,  or  to  meters  and  a  decmial  of  a  meter : 

1.  5  Km.  6.  6Hm.  11.   125  dm.  16.  2400  mm. 

2.  3.5  Km.  7.  45  Dm.  12.  12.5  dm.         17.  354.6  mm. 

3.  15  Km.  8.  1.8  Hm.  13.  1.25  dm.         18.  11.75  cm. 

4.  21.7  Km.  9.  12.3  Dm.         14.  175  cm.  19.  11.75  dm. 

5.  15.08  Km.      10.  11.15  Dm.       15.   1450  cm.         20.  1405  cm. 

Change  to  meters  or  to  decimals  of  a  meter : 

21.  3  Km.,  5  Hm.  24.   4  m.,  5  dm.  27.   45  dm.,  45  cm. 

22.  5  Hm.,  8  Dm.  25.    15  m.,  8  dm.  28.    15  dm.,  57  cm. 

23.  4  Km.,  4  Dm.  26.    35  m.,  25  cm.  29.    25  cm.,  75  dm. 

*. 

Express  in  meters  :  Express  in  feet : 

30.  10  ft.  33.  35.5  in.  36.  12  m.  39.  2500  cm. 

31.  32  ft.  34.  110  in.  37.  15.75  m.        40.  2500  dm. 

32.  5.6  ft.  35.  2  ft.  5.5  in.  38.  4.875  Dm.     41.   11250  mm, 

Change  to  miles  :  Change  to  kilometers  : 

42.  4  Km.  44.  10.5  Km.         46.   100  mi.  48.  .025  mi. 

43.  12.5  Km.        45.  125.5  ICm.       47.   125  mi.  49.  .00125  mi. 


METRIC  SYSTEM 


265 


Metric  Measures  of  Surface 

The  Square  Meter  is  the  standard  unit  of  surface  measure  in  the 
metric  system. 

The  square  meter  is  a  square  whose  side  is  1  meter  long. 

If  the  sides  of  the  square  meter  are  each 
divided  into  10  equal  parts,  each  part  is 
1  decimeter  long.  If  lines  are  drawn  con- 
necting the  points  of  division  on  opposite 
sides,  the  square  meter  is  divided  into  100 
equal  parts,  and  since  the  sides  of  each  of 
these  100  squares  are  each  1  decimeter 
long,  the  square  meter  is  equal  in  area  to 
100  square  decimeters. 

In  like  manner,  each  square  decimeter  may  be  divided  into  100 
equal  squares,  each  of  which  is  a  square  centimeter.  Moreover, 
the  square  constructed  on  a  length  equal  to  10  meters  would  give 
100  square  meters,  or  a  square  Dekameter,  and  the  process  could 
be  repeated  to  obtain  larger  square  units  of  measure. 

From  this  principle  of  division  or  multiplication  of  the  standard 
square  unit  of  measure  we  have  the  table  for 


:. 


Metric  Measures  of  Surface 


100  square  millimeters 

=  1  square  centimeter 

abbreviated 

sq. 

cm. 

100  square  centimeters 

=  1  square  decimeter 

sq. 

dm. 

100  square  decimeters 

=  1,  square  meter 

sq. 

m. 

100  square  meters 

=  1  square  dekameter 

sq. 

Dm. 

1.00  square  dekameters 

=  1  square  hektometer 

sq. 

Hm. 

100  square  hektometers 

=  1  square  kilometer 

sq. 

Km. 

Approximate  equivalents  in  terms  of  English  Standards. 


1  sq.  m.     =1.196  sq.  yd. 
1  sq.  Km.  =  .386  sq.  mi. 


1  sq.  yd.    =.8361  sq.  m. 
1  sq.  mi.   =2.59  sq.  Km. 


266  METRIC    SYSTEM 

The  square  meter  is  used  for  measuring  surfaces  like  floors, 
walls,  etc. 

The  square  kilometer  is  used  for  measuring  large  land  areas. 

For  small  land  areas  the  square  dekameter  is  the  principal  unit 
of  measure  and  is  called  the  Are  (pronounced  ar) .  For  land  areas 
it  is  customary  to  use  the  table  in  the  following  form  : 

100  ares         =1  centare 
#  100  centares  =  1  hektare 

Changing  from  One  Denomination  to  Another  Denomination. 

The  table  shows  that  each  square  unit  of  measure  is  100  times  the 
preceding  square  unit  of  measure.  Therefore,  to  change  from  one 
denomination  to  the  next  higher  denomination  we  move  the  deci- 
mal point  two  places  to  the  left. 

Thus :        4500  sq.  cm,  =45  sq.  dm.  =.45  sq.  m. 

We  may  also  change  from  one  denomination  to  the  next  lower 
denomination  by  moving  the  decimal  point  two  places  to  the  right. 
Thus  :  12  sq.  m.  =  1200  sq.  dm.  =  120000  sq.  cm. 

BLACKBOARD    PRACTICE 

Change  to  square  meters  : 

1.  125  sq.  Km.         4.    124.5  sq.  Km.  7.    15625  sq.  mm. 

2.  160  sq.  Hm.         5. 

3.  250  sq.  Dm.         6.    1250.05  sq.  Dm.  9.    154500  sq.  dm. 

Express  in  square  yards 

10.  100  sq.  m. 

11.  11.5  sq.  m. 

Express  in  square  miles  : 

14.  12.5  sq.  Km. 

15.  24.1  sq.  Km. 

Metric  Measures  of  Volume 

The  Cubic  Meter  is  the  standard  unit  of  volume  measure  in  the 
metric  system. 


375.25  i 

3q.  Hm. 

8. 

254( 

1250.05 

sq.  Dm. 

9. 

1541 

12. 

1.125 

sq. 

m. 

13. 

.125  sq.  Km. 

16. 

.0125 

sq. 

Km. 

17. 

11375 

sq. 

,  m. 

METRIC  SYSTEM 


267 


The  cubic  meter  is  a  cube  whose  edge  is  1  meter  long. 

If  the  edges  of  the  cubic  meter  are  each  divided  into  10  equal 
parts,  each  part  is  1  decimeter  long.  If  the  cubic  meter  were 
then  cut  by  planes  passing 
through  the  points  of  divi- 
sion of  each  edge,  and  par- 
allel to  the  three  faces  that 
meet  in  any  point,  the  cubic 
meter  would  be  cut  into 
1000  cubes,  each  small  cube 
being  1  decimeter  on  each 
edge. 

In  Uke  manner  each  cubic 
decimeter  could  be  cut  by 
planes  into  1000  smaller 
cubes,  each  of  which  would  be  1  cubic  centimeter.  The  cubic 
centimeter  could  be  cut,  furthermore,  into  1000  smaller  cubes, 
each  one  a  cubic  millimeter.     We  have,  therefore,  the  table  for 

Metric  Measures  of  Volume 


1000  cubic  millimeters  (cu.  mm.)  =  1  cubic  centimeter  abbreviated  cu.  cm. 
1000  cubic  centimeters  =1  cubic  decimeter  "  cu.  dm. 

1000  cubic  decimeters  =1  cubic  meter  "  cu.  m. 


(Measures  larger  than  the  cubic  meter  have  no  practical  use.) 

Changing  from  One  Denomination  to  Another  Denomination. 
Each  unit  in  the  table  of  volume  measure  is  1000  times  the  pre- 
ceding unit.     Therefore, 

To  change  from  one  denomination  to  the  next  higher  denomina- 
tion move  the  decunal  point  three  places  to  the  left. 

To  change  from  one  denomination  to  the  next  lower  denomina- 
tion move  the  decimal  point  three  places  to  the  right. 

Thus  :         4575  cu.  cm. =4.575  cu.  dm. 

And :  15.658  cu.  m.  =  15658  cu.  dm.  =  15658000  cu.  cm. 


268 


METRIC   SYSTEM 


BLACKBOARD    PRACTICE 

Change  to  higher  denominations  : 

1.  1500  cu.  cm.,  150000  cu.  cm. 

2.  35000  cu.  mm.,  125000  cu.  dm. 

3.  4570000  cu.  mm.,  12575000  cu.  mm. 

Change  to  lower  denominations  : 

4.  15  cu.  m.,  150  cu.  dm. 

5.  275  cu.  m.,  4500  cu.  dm. 

6.  15750  cu.  cm.,  354000  cu.  cm. 


Metric  Measures  of  Capacity 

The  Liter  is  the  standard  unit  of  capacity  measure,  either  dry 
or  Uquid,  in  the  metric  system. 

A  standard  Hter  is  a  cubical  box  whose  inside  edges  are  each  1 
decimeter  long.     Therefore,  the  liter  is  a  cubic  decimeter. 

Since  each  edge  of  the  cubic  decimeter  is  10  centimeters  long, 
the  liter  contains  1000  cubic  centimeters. 

Metric  Measures  of  Capacity 


10  milliliters  (ml.)  =1  centiliter 

abbreviated  cl. 

10  centiliters           =1  deciliter 

dl. 

10  deciliters            =1  liter 

1. 

10  liters                   =  1  dekaliter 

Dl. 

10  dekaliters           =  1  hektoliter 

HI. 

Convenient  approximate  equivalents  in  terms  of  English  Standards. 

1  liter  =  1.0567  liquid  quarts  1  hektoliter  =2.8375  bushels 

1  liter  =  .908  dry  quart  1  hektoliter  =26.417  gallons 

The  liter  is  used  for  measuring  liquids  or  small  fruits  in  small  quantities- 
The  hektoliter  is  used  for  measuring  large  quantities. 


METRIC  SYSTEM 


269 


BLACKBOARD    PRACTICE 


Change  to  higher  denominations 

1.  15  1,  4.    3500  ml. 

2.  12.5  1.  5.    254.75  dl. 

3.  500  cl.  6.    254.75  Dl. 

Express  in  liquid  quarts  : 

13.  10  1.  16.    15  dl. 

14.  12.5  1.        17.    1.4  HI. 

15.  175.2  1.       18.    25.8  Kl. 

Express  in  bushels : 

25.  5.5  HI.       27.    175  1. 

26.  12.1  HI.     28.    25000  dl. 


Change  to  lower  denominations : 

7.  35  Kl.  10.    147.5  1. 

8.  45.8  HI.         11.   35.125  1. 

9.  175.25  Dl.     12.   45.25  cl. 

Express  in  dry  quarts  : 

19.  35  1.  22.    175  dl. 

20.  15.8  1.  23.    25.125  Dl. 

21.  250.75  dl.      24.    15000  cl. 

Express  in  hektoliters : 

29.  15  bu.  31.    320  pk. 

30.  75.5  bu.         32.    1600  qt. 


Metric  Measures  of  Weight 

The  Gram  is  the  standard  unit  of  weight  measure  in  the  metric 
system. 

The  gram  was  established  by  taking  the  weight  of  1  cubic  centi- 
meter of  water  as  a  standard  of  measure. 

Therefore, 

since  1  Hter  =  1  cubic  decimeter  =  1000  cubic  centimeters, 

and 

since  1  cubic  centimeter  of  water  =  1  gram  of  weight, 
it  follows  that 

I  liter  of  water  weighs  looo  grams  or  i  kilogram 

The  advantage  of  this  relation  lies  in  the  ease  with  which  we  may 
change  from  a  standard  Ciuantity  to  a  standard  weight  by  merely 
changing  the  name  of  the  unit. 

Thus  :  150  cu.  cm.  water  weighs  150  grams 
2.5  1.  water  weighs  2.5  Kg. 


270 


METRIC    SYSTEM 


Metric  Measures  of  Weight 


10  milligrams  (mg.) 

=  1  centigram 

abbreviated  eg. 

10  centigrams 

=  1  decigram 

<ig. 

10  decigrams 

=  1  gram 

g. 

10  grams 

=  1  dekagram 

Dg. 

10  dekagrams 

=  1  hektogram 

Hg. 

10  hektograms 

=  1  kilogram 

Kg. 

Large  quantities  of  heavy  commodities  necessitate  units  of  higher 
denominations  than  the  kilogram.     These  are  : 

10  kilograms  =  1  myriagram  Mg. 
100  kilograms  =  1  metric  quintal  Q. 
1000  kilograms  =  1  metric  ton  T. 

Convenient  approximate  equivalents  in  terms  of  English  standards. 

1  gram  =  15.432  grains  1  kilogram  =2.20462  pounds 

1  metric  ton  =2204.621  pounds 

The  gram  is  used  in  the  sciences,  in  weighing  drugs,  medicines, 
etc.,  the  kilogram  is  used  for  weighing  commodities  for  which  the 
English  standard  uses  the  pound,  and  the  metric  ton  is  used  for 
heavy  articles  in  large  amounts. 


BLACKBOARD   PRACTICE 


Change  to  pounds : 

13.  15  Kg.    15.  12.5  Kg. 

14.  1.25  Kg.  16.  12.5  Dg. 


7.  1500  mg. 


Change  to  grams : 

1.  12  Kg.    4.  75.8  Hg. 

2.  15.5  Kg.   5.  157.1  Dg.    8.  1750  eg. 

3.  1.75  Kg.   6.  154.25  Kg.   9.  3750  dg. 


10.  17500  mg. 

11.  187500  mg. 

12.  187500  eg. 


17.  157.1  Hg.  19.  35.125  Dg. 

18.  157100  g.  20.  120000  eg. 


METRIC  SYSTEM  271 

Finding  the  Given  Weight  of  Any  Given  SoUd  by  comparing  its 
weight  with  the  weight  of  the  same  quantity  of  water  is  possible 
through  apphcation  of  the  metric  system.  By  careful  experi- 
ments scientists  have  determined  the  relation  of  the  weight  of 
common  metals,  liquids,  etc.,  to  the  weight  of  the  same  volume  of 
water. 

Thus  :    Cast  Iron  is  known  to  be  7.2  times  as  heavy  as  water. 
Lead  is  known  to  be  11.37  times  as  heavy  as  water. 
Alcohol  is  known  to  be  .792  of  the  weight  of  water,  etc. 

These  known  relations,  or  ratios,  between  the  weight  of  a  sub- 
stance and  the  weight  of  the  same  quantity  of  water  enable  us  to 
calculate  by  simple  multiplication  the  weight  of  any  quantity  of  a 
substance. 

Illustrations : 

1.  Find  the  weight  of  12.5 1.  of  milk,  if  milk  is  1.03  times  as  heavy 
as  water. 

1  1.  of  water  weighs  1000  g.     Hence,  12.5  1.  w^ater  weighs  12500  g. 

But  milk  is  1.03  times  the  weight  of  water. 

Therefore,  12500  g.  milk  weighs  (1.03X12500)  g.  or  12875  g.     Result. 

2.  Find  the  weight  of  a  bar  of  steel  1.5  m.  long,  3  cm.  wide,  and 
1  cm.  thick,  if  steel  is  7.8  times  the  weight  of  water. 

We  find  first  the  number  of  cu.  cm.  in  the  steel  bar. 

(1.5  XlOO)  X3  Xl  =450,  the  number  of  cu.  cm.  in  the  volume  of  the  bar. 

Now  the  weight  of  450  cu.  cm.  of  water  =450  g. 

And  the  steel  is  7.8  times  as  heavy  as  water. 

Hence,  the  weight  of  the  bar  =7.8X450  g.  =3510  g.     Result. 

The  ratio  of  the  weight  of  a  given  substance  to  the  weight  of 
the  same  volume  of  water  is  called  the  Specific  Gravity  of  the 
substance. 


272 


METRIC    SYSTEM 


Specific  Gkavitt  op  Common  Substances 


Steel      .     . 

.       7.8 

Copper 

.       8.8 

Lead 

.     11.3 

Gold     .     . 

.     19.3 

Platinum  . 

.     21.1  ' 

Yellow  Pine 
White  Oak 
Alcohol  .     . 
Machine  Oils 
Rubber  . 


.70 

.75 
.79 
.92 
.92 


BLACKBOARD   PRACTICE 


Find  the  weight  of : 

1.  100  cu.  dm.  of  steel. 

2.  120  cu.  dm.  of  gold. 


9.   5000  cu.  cm.  of  yellow  pine. 
10.    150000  cu.  dm.  of  white  oak. 


3.  15.125  cu.  dm.  of  copper.     11.   2500  Kl.  of  alcohol. 

4.  100000  cu.  cm.  of  lead.        12.    10000  Dl.  of  machine  oil. 

5.  25000  cu.  cm.  of  platinum.  13.    150000  cu.  dm.  of  rubber. 

6.  10000  cu.  cm.  of  copper.      14.    200000  cu.  dm.  of  alcohol. 

7.  156500  cu.  cm.  of  lead.        15.    15000  cu.  dm.  of  yellow  pine. 

8.  345000  cu.  cm.  of  gold.       16.   35000  cu.  cm.  of  white  oak. 


Table  op  Equivalents 

Metric  to  Common 

Common  to  Metric 

1  m.        =39.37  in. 

1yd.           =.9144  m. 

1  Km.     =.62137  mi. 

1  mi.           =1.60935  Km. 

1  sq.  m.  =1.196  sq.  yd. 

1  sq.  yd.     =.836  sq.  m. 

1  Ha.      =2.471  A. 

1  A.             =  .4047  Ha. 

1  cu.  m.  =1.308  cu.  yd. 

1  cu.  yd.     =  .765  cu.  m. 

11.          =  .908  qt.  (dry) 

Iqt.  (dry)  =1.1012  1. 

11.          =1.0567  qt.  (liq.) 

1  qt.  (liq.)  =.946361. 

1  HI.       =2.8377  bu. 

Ibu.           =.35239  HI. 

1  Kg.      =2.2046  lb.  (av.) 

1  lb.  (av.)  =.45359  Kg. 

1  M.  T.=  1.1023  T. 

IT.             =.90718  M.T. 

METRIC  SYSTEM  273 

Miscellaneous  Applications  of  Metric  System 

1.  The  ''  bore/'  or  inside  diameter,  of  a  rifle  barrel  is  7  mm. 
What  is  the  diameter  in  inches  ? 

2.  The  Panama  Canal  is  approximately  40.5  miles  long.  What 
is  the  length  of  the  canal  in  kilometers  ? 

3.  Three  successive  distances  measured  along  a  straight  hne 
were  5.14  Km.,  275  m.,  and  31.25  Hm.,  respectively.  What  was 
the  total  distance? 

4.  100  liters  of  ohve  oil  cost  a  dealer  $.75  per  liter.  Find  the 
amount  of  gain  he  made  when  he  sold  the  oil  for  $.90  per  quart. 

5.  A  rectangular  plot  is  24  meters  long  and  15  meters  wide. 
W^hat  is  the  area  of  the  plot  in  square  meters  and  in  square  feet  ? 

6.  A  consignment  of  100  cars  of  coal  averaging  50  tons  each  is 
shipped  by  an  exporter.  How  many  metric  tons  were  there  in 
the  consigmnent  ? 

7.  The  Great  Pyramid  of  Egypt  has  a  square  base  764  feet  on  a 
side,  and  its  altitude  is  480  feet.     Find  the  volume  in  cubic  meters. 

8.  How  many  pint  bottles  must  be  provided  by  a  dealer  for  the 
contents  of  a  cask  containing  2  kiloliters  of  olive  oil? 

9.  Broad  street,  Philadelphia,  is  100  feet  wide  between  the 
curbstones.  Express  this  width  in  meters,  also  in  a  decimal  part 
of  a  kilometer. 

10.  A  barrel  of  flour  weighs  196  pounds.  How  many  kilograms 
of  flour  are  there  in  a  consignment  of  800  barrels  of  flour  ? 

11.  A  building  lot  20  meters  wide  and  90  meters  deep  is  sold  at 
the  rate  of  $1200  per  acre.     What  amount  is  received  for  the  lot? 

12.  An  importer  places  an  order  for  15  gallons  of  perfume,  and 
the  foreign  dealer  bills  it  in  liters.  For  how  many  liters  was  the 
bill  written? 

13.  If  3^ou  find  that  the  length  of  your  average  step  in  walking 
is  30  inches,  how  many  steps  will  you  take  in  going  over  a  distance 
of  1  kilometer? 


274  METRIC   SYSTEM 

14.  A  druggist  is  required  to  compound  a  quantity  of  capsules, 
each  one  to  contain  12  eg.  of  a  certain  drug.  He  used  1.2  Kg.  of 
the  drug.     How  many  capsules  did  he  make  ? 

15.  The  French  cable  between  New  York  and  Brest  is  3305.164 
miles  long.  What  is  the  length  of  this  cable  in  meters  ?  In  kilo- 
meters ? 

16.  The  specific  gravity  of  a  certain  grade  of  olive  oil  is  .915. 
Find  the  weight  in  kilograms  of  twenty-five  cans  of  oil,  each  can 

» 

containing  1.3  1. 

17.  Eight  yards  of  silk  in  a  dress  cost  the  importer  $2.00  per 
meter.  If  he  received  $3  per  yard,  what  was  the  amount  of  his 
profit  on  the  goods  ? 

18.  A  liter  of  glue  weighs  2.0  Kg.  What  is  the  weight  of  the 
glue  contained  in  a  full  tank  that  is  known  to  hold  240  gallons  ? 

19.  The  distance  from  Brussels  to  Paris  is  326  Km.,  and  the 
railway  fare  is  approximately  19.3  centimes  per  mile.  Find  the 
fare  between  the  cities. 

20.  A  French  express  train  travels  75  Km.  in  1  hour,  and  a  New 
York  Central  express  train  travels  75  miles  in  the  same  time. 
How  many  more  miles  per  hour  does  the  faster  train  travel  ? 

21.  A  foreign  builder  orders  from  the  United  States  Steel 
Corporation  a  plate  girder,  giving  its  exact  length  as  10.125  m. 
Find  the  exact  length  of  the  girder  in  feet  and  inches  to  the  nearest 
hundredth  of  an  inch. 

22.  An  imported  plate  glass  mirror  is  56  cm.  long  and  35.5  cm. 
wide.  Find  the  number  of  feet  of  molding  required  to  frame  the 
mirror,  the  molding  being  2  inches  wide.  (Allow  for  the  loss  in 
making  the  corners.) 

23.  When  empty  a  tank  weighs  15.75  Kg.,  and  when  filled  with 
w^ater  the  total  weight  of  the  tank  and  the  water  is  142  Kg.  How 
many  liters  of  water  will  the  tank  contain  ?     How  many  gallons  ? 


METRIC  SYSTEM  275 

24.  The  diameter  of  an  automobile  wheel  is  28  inches,  and  the 
tire  is  3.5  inches  in  diameter  when  allowance  is  made  for  flattening. 
How  many  turns  will  this  wheel  make  in  going  over  a  distance  of 
1  kilometer? 

25.  Brass  is  composed  of  60%  copper  and  40%  zinc.  How  many 
kilograms  of  each  element,  copper  and  zinc,  are  there  in  a  bar  of 
brass  which  weighs  45,000  g.? 

26.  The  duty  on  100  1.  of  olive  oil  was  $15.60,  and  the  cost  of 
the  cartage  $1.25.  The  oil  cost  $.60  per  liter  and  was  sold  for 
$3.50  per  gallon.  What  was  the  amount  of  profit  made  by  the 
importer? 

27.  A  tank  of  oil  whose  specific  gravity  is  .91  weighs  145  Kg. 
The  empty  cask  weighs  44.092  pounds.  How  many  liters  of  oil 
are  there  in  the  cask,  and  how  many  quarts  ? 

28.  Scientists  have  determined  that  a  liter  of  air  weighs  1.292  g. 
At  that  rate  calculate  the  weight  of  the  air  in  a  room  thirty  feet 
long,  22  feet  wide,  and  12  feet  high,  giving  the  weight  in  kilos  and 
in  pounds. 

29.  An  automobile  uses  an  average  of  one  gallon  of  gasohne  to 
every  sixteen  miles  of  a  journey.  At  the  same  rate  determine  how 
many  kilometers  the  automobile  would  run  on  one  liter  of  gasoline. 

30.  A  quantity  of  silk  cost  in  Paris  $2.80  per  meter,  and  the  duty 
was  45%.  The  total  expense  for  shipping,  freight,  insurance,  etc., 
amounted  to  $.60  per  meter.  At  what  price  per  yard  must  the 
importer  sell  the  silk  in  order  to  make  a  profit  of  30%  ?  r 

31.  Compare  the  labor  of  finding  the  number  of  liters  in  a  tank 
5  m.  long,  3  m.  wide,  and  15  dm.  deep,  with  the  labor  oi  finding 
the  number  of  gallons  in  a  tank  16  feet  long,  10  feet  wide,  and 
1  yard  deep.  Time  yourself  on  the  work  of  finding  each  result. 
Find  what  per  cent  of  the  time  needed  for  the  longer  process  is  the 
time  needed  for  the  shorter  one. 


276 


CUBE   ROOT 


(a) 


CUBE   ROOT 

The  Formation  of  a  Cubic  Solid. 

Suppose  that  we  have  in  (a)  a  cube  whose  edge  is  10  inches  long. 

Then  any  three  adjacent  faces  have  areas  measur- 
ing 100  square  inches  each. 

(The  volume  of  the  solid  is  1000  cubic  inches.) 

Suppose,  further,  that    we   wish    to    enlarge    the 
given  cube  to  a  cube  whose  edge  shall  be  12  inches, 
that  is,  2  inches  longer  than  the  cube  in  (a).     We 
can  accomphsh  this  by  building  upon  three  square  faces  that  are 
adjacent. 

In  (6)  we  have  built  on  each  of  three  faces  a  new  volume  2 
inches  thick. 

These  three  additions  are  built  upon  square  faces  10  inches  by 
10  inches,  hence  each  new  volume  is  made  up 
of  10x10x2  cubic  inches. 

(The  volume  thus  added  is  600  cubic  inches.) 

The  solid  as  it  now  stands  has  three  unfilled 
**  notches,"  each  of  which  is  10  inches  long, 
2  inches  wide,  and  2  inches  deep.  Into  these 
notches  we  msiy  build,  therefore,  three  square  prisms. 

In  (c)  we  have  built  in  the  three  solids  necessary  to  fill  up  the 
notches. 

These   three   prisms  are    each    10   inches  long, 
2  inches  wide,  and  2  inches  deep. 

(The  volume  thus  added  is  120  cubic  inches.) 

Excepting  the  small  cubical  portion  where  the 
three  prisms  come  together,  the  larger  cube  is  now 
complete.     This  small  portion  is  2  inches  long, 
2  inches  wide,  and  2  inches  deep.     In  (d)  this  small  remaining 
volume  has  been  added,  and  the  new  cube  is  complete. 

(The  volume  thus  added  is  8  cubic  inches.) 


CUBE  ROOT 


277 


'd) 


It  is  well  to  remember  at  this  point  that  tht 
process  of  increasing  the  original  cube  to  a  larger 
cube  required  the  addition  of  three  square  prisms, 
three  other  square  prisms  and  a  cube. 

The  process  of  finding  the  cube  root  of  a  number 
depends  upon  the  principles  that  governed  us  in 
building  the  cube  just  illustrated,  but  the  steps  ol 
the  process  will  be  reversed  in  order. 

The  Cube  of  a  Number. 

The  cube  of  a  number  is  the  product  obtained  by  using  the 
number  three  times  as  a  factor. 

In  the  following  illustration  the  cube  of  12  is  obtamed  in  twa 
ways,  first,  by  multiplying  12x12x12  in  the  ordinary  way;  and, 
second,  by  finding  the  product  of  (10+2)  by  (10+2)  by  (10+2). 

12=  10+2 

12=  10+2 

24  = 
120  = 
144  = 
12  = 
288=  (102X2) +2(10X22) +2-* 

1440  =  10^+2(102X2)+   (10X22) 
1728  =  103  +3(102  X2)  +3(10  X22)  +2* 

It  will  be  observed  that  the  result  is  made  up  of  four  parts,  andi 
that  they  are : 

103  =1000 

3(102X2)=  600 
3(10X22)=   120 

23  =8 


(10X2) +2* 
10^+   (10X2) 
102 +2(10X2) +2* 
10+2 


1000+600+120+8  =  1728      . 

Observe  that 

103        =1000  corresponds  to  jB^re  (a) 

3(102x2)=  600  corresponds  to  the  additions  that  give  ihy 

3(10x22)=  120  corresponds  to  the  additions  that  give  (c) 

2'          =8  corresponds  to  the  additions  that  give  {dy 


278  CUBE   ROOT 

The  student  should  go  through  the  same  process  of  reasoning 
with  a  cube  of  different  dimensions.  For  example,  take  2744,  and 
make  the  drawings  that  result  when  the  cube  first  removed  is 
10  units  on  each  edge,  and  the  solid  additions  are  each  4  units 
thick. 

With  a  knowledge  of  the  relation  of  a  cubic  solid  to  a  numerical 
cube  we  are  ready  to  learn  the  process  of  extracting  cube  root. 

The  General  Method  for  Finding  Cube  Root 

The  Relation  between  the  Number  of  Places  in  a  cube  and  the 
number  in  the  corresponding  cube  root  will  be  seen  from  the 
following. 

The  largest  number  having  one  place  is  9.    9- =  729,  three  places. 

The  largest  number  having  two  places  is  99.  99^  =  970299,  six 
places. 

The  largest  number  having  three  places  is  999.  999^  =  997002999, 
nine  places. 

That  is,  a  number  having  either  one,  two,  or  three  places  may 
have  in  its  cube  as. many  as  three,  six,  or  nine  places,  respectively. 

If,  therefore,  a  number  is  considered  as  "  separated  into  periods 
of  three  places  each,"  the  number  of  such  periods  obtained  will 
equal  the  number  of  places  in  the  cube  root  that  is  sought. 

For  example:  112678587  written  thus,  112  678  587,  gives  three 
periods,  and  its  cube  root,  483,  has  three  places. 

The  period  at  the  left  need  not  have  three  places. 

For  example,  the  cube  root  of  15625,  or  15  625,  is  25. 

And  the  cube  root  of  22188041,  or  22  188  041,  is  281. 

As  in  square  root  (p.  155),  the  cube  root  of  a  decimal  number  is 
obtained  by  the  process  used  for  the  cube  root  of  integers,  care  be- 
ing taken  to  "  point  off  "  properly  in  the  root. 

The  cube  of  a  decimal  of  one  place  has  three  decunal  places  ;  the 
cube  of  a  decimal  of  two  places  has  six  decimal  places,  etc. 


CUBE  ROOT 


279 


Finding  the  Cube  Root  of  a  Number. 
Illustration : 


Find  the  cube  root  of  39304. 


I.  30^ 
II.  3(30)2       =2700 

III.  3X30X4=  360 

IV.  42  =     16 

3076 
V.  3076X4    = 


39  304130+4 
27  000 


12  304 


12  304 


Explanation : 

Beginning  at  the  decimal  point, 
separate  the  given  cube  into 
periods  of  three  figures  each. 

The  first  period  is  39000. 

The  greatest  cube  in  39000  is 
27000. 

The  cube  root  of  27000  is  30. 

Write  30"  in  the  root. 

Subtract  2700 'from  39304. 


Reference  to  the  figures  will  help  you  as  you   follow   the  steps  from 
this  point  on. 


(a) 


(c) 


0 


(d) 


When  we  subtract  27000  we  have  removed  the  largest  possible  cube 
that  we  know  by  inspection  Ues  in  the  given  solid. 

Suppose  that  (a)  represents  the  cube  27000  that  we  have  removed. 
(See  Une  I.) 

Then  the  remaining  volume,  12304  cubic  units,  is  represented  by  (b). 

We  must  now  find  the  approximate  thickness  of  the  volume  represented 
by  our  12304  cubic  units,  and  we  note  that  the  area  of  any  one  inside  face 
in  (6)  is  30-  units,  or  900  square  units. 

We,  therefore,  cU\dde  the  enthe  volume,  12304  square  units,  bj'-  the 
known  area  of  all  three  faces,  or  by  (3  X900)  square  units,  or  2700  square 
units.  (See  line  II.)  The  quotient  is  apparently  4,  which  we  \VTite  in  the 
root  as  a  trial. 

Having  considered  the  volume  of  the  three  faces,  there  remains  to  be 
considered  the  three  prisms  that  are  left,  as  in  (c). 


280 


CUBE   ROOT 


Each  prism  is  30  units  long,  and  we  have  assumed  them  to  be  4  units 
thick;  hence  the  total  area  of  these  inside  faces  is  apparently  3(30X4) 
square  units,  or  360  square  units.     (See  line  III.) 

With  the  three  prisms  disposed  of  there  remains  the  small  solid  (d) 
the  area  of  whose  face  is  (4X4)  square  units  since  we  have  assumed  its 
thickness  in  two  dimensions  as  4  units.  This  completes  the  assumed  areas 
and  we  write  4^.     (See  line  IV.) 

Adding  the  three  areas,  lines  II,  III,  and  IV,  we  have  a  total  area  of 
3076  square  units. 

Multiplying  this  area  by  our  assumed  thickness  we  have  a  volume 
of  (4X3076)  cubic  units.  This  volume,  subtracted  from  12304  cubic 
units,  gives  a  remainder  of  0. 

The  following  examples  will  further  illustrate  the  process,  and 
the  student  will  familiarize  himself  with  the  method  by  going 
carefully  through  each  step  in  each  illustration. 

It  will  be  observed  that  (1)  a  cube  whose  root  consists  oi 
three  figures  is  obtained  by  repeating  the  process  to  obtain 
root  figures  after  the  second ;  and  (2)  the  cube  root  of  a  decimal 
number  is  obtained  by  working  as  in  whole  numbers,  pointing 
off  at  the  end  of  the  process  the  proper  decimal  places  in  th^ 
root. 

Illustrations : 
1.   Find  the  cube  root  of  14706125. 


14  706  125  ! 

245     Res 

'Ult. 

203 

8  000 

3X202 

1200 

6  706 

3X20X4   = 

240 

Note  that  iii  each  use 

42 

16 
1456 

of   the    trial    divisor   wf 
consider  it  to  be  tens  ir 

4X1456      = 

5  824 

882  125 

the    first    division,   hun 

3X2402      = 

172800 

dreds  in  the  second  divi 

3X240X5  = 

3600 

sion,  etc. 

52 

25 
176425 

• 

5X176425  = 

882  125 

CUBE  ROOT 


281 


2.   Find  the  cube  root  of  1175.45  to  two  decimal  places. 
Pointing  off  from  the  decimal*  point,  and  annexing  four  ciphers 
for  the  necessary  decimal,  we  have 

1052 


1175.450  000 

10' 

1000 

3X102          =         300 

175 

The    trial    divisor 

being  too  large,  bring 

down  another  period, 

and  place   a   "0"   in 

the  root. 

175  450 

3X1002         =     30000 

3X100X5    =       1500 

52                  =           25 

5X31525      = 

157  625 

3X15002       =6750000 

17  825  000 

3X1500X2=       9000 

22                  =4 

2X6759004  = 

13  518  008 

The  figures  in  the  required 
root  are  1052. 

Pointing  off  two  places  for 
the  two  periods  in  the  decimal, 
we  have 

10.52+     Result. 


From  the  foregoing  illustrations  we  may  state  the  general 

Rule :  Beginning  at  the  decimal  point,  separate  the  given  number 
into  periods  of  three  figures  each. 

Find  the  greatest  cube  in  the  fii^st  period  at  the  left,  subtract  this  cube 
from  the  first  period,  and  write  its  cube  root  for  the  first  figure  of  the 
result.     Annex  the  next  period  to  the  remainder  for  a  dividend. 

Take  three  times  the  square  of  the  root  already  found,  considered  as 
tens,  and  divide  the  dividend  bij  this  trial  divisor. 

The  quotient  will  be  the  second  figure  of  the  root. 

To  this  partial  divisor  add  three  times  the  product  of  the  first  part  of 
the  root,  considered  as  tens,  by  the  second  part ;  and  add  also  the  square 
of  the  second  part.     Their  sum  will  be  the  complete  divisor. 

Multiply  the  complete  divisor  by  the  second  part  of  the  root,  and 
subtract  the  product  from  the  dividend. 

Repeat  this  process  in  the  same  order  until  all  the  figures  of  the  root 
have  been  found. 


282 


CUBE   ROOT 


BLACKBOARD    PRACTICE 

Find  the  cube  root  of  : 


1.  3375. 

2.  9261. 

3.  29791. 

4.  54872. 

5.  46656. 


6.  68921. 

7.  79507. 

8.  85184. 

9.  157464. 
10.  314432. 

Find,  to  two  decimal  places,  the  cube  root  of : 

21.  1500.         23.  15000.        25.    .00675.       27. 

22.  28000.       24.  11.198.       26.    .0008.         28. 


11.  658503. 

12.  941192. 

13.  8242408. 

14.  7880599. 

15.  2248.091. 


16.  7.529536. 

17.  .004913. 

18.  141.420761. 

19.  .065939264. 

20.  124251.499. 


3. 
5* 

18* 


oq      15 


INDEX 


Accounts,  175 

The  Cash,  7 
Altitude 

of  a  Cone,  239 

of  a  Cylinder,  170,  235 

of  a  Prism,  232 

of  a  Pyramid,  237 
Amount 

of  a  Bill,  87 

of  Principal  and  Interest,  100 
Analysis,  38 

Direct,  38 

Indirect,  38 
Antecedent  of  Ratio,  138 
Assessed  Valuation,  192 
Assessment,  201 
Assessor,  192 
Association,  Building  and  Loan,  199 

Balance,  8,  175 
Bank,  109 

Commercial,  109 

Discount,  115 

Draft,  133 

Federal  Reserve,  109,  126 

National,  109 

Private,  109 

Savings,  105,  109,  124 

State,  109 
Base 

in  Percentage,  61 

of  a  Cylinder,  170 
Beneficiary,  188 
Bills,  9,  179 

Net  amount  of,  87 

Receipting,  9 
Bins,  Capacity  of,  29 
Bond,  107,  208 

Corporation,  208 

Coupon,  208 

Government,  208 

Liberty  Loan,  107 

Municipal,  208 

Registered,  208 


Book,  Check,  110 

Pass,  110 
Broker,  Stock,  202 
Brokerage,  203 
Building  and   Loan   Association. 

199 

Capacity  of  Bins,  29 
Carpeting,  24 
Cash  Account,  7 

Discount,  87 

on  hand,  8 
Certificate  of  Sto(;k,  201 
Certified  Check,  132 
Check,  110 

Bank,  112 

Book,  110 

Certified,  132 

Personal,  132 
Checking,  42 
Circle,  165 

Circumference  of,  165 

Diameter  of,  165 

Radius  of,  165 
Circumference 

of  a  circle,  165 

of  a  sphere,  242 
Collector,  Tax,  193 
Commercial  Bank,  109 
Commercial  Discount,  87 
Commission,  203 
Common  Shares,  201 
Company,  Stock,  201 
Compound  Interest,  120 
Concrete,  33 
Corporate  Bond,  208 
Corporation,  201 
Cost,  77 

Cost  Marks,  Private,  82 
Coupon  Bonds,  208 
Credits,  175 
Cube,  148 

Root,  150 
Cubic  Meter,  267 

283 


284 


INDEX 


Cylinder,  170,  235 
Altitude  of,  35,  170 
Bases  of,  170 
Circular,  235 

Lateral  Surface  of,  170,  235 
Total  Surface  of,  235 
Volume  of,  170,  236 

Day  of  Maturity,  245 
Daybook,  175,  176 
Debit  Side,  7 
Debits,  175 
Deposit  Slip,  110 
Diagonals  of  a  Square,  161 
Diameter  of  a  Sphere,  242 

of  a  Circle,  165 
Direct  Analysis,  38 
Discount,  86 

Bank,  115 

Cash,  87 

Commercial,  87 

In  Exchange,  136 

Series,  91 

Term  of,  115 

Trade,  86 
Direct  Tax,  192 
Dividend,  201 
Draft,  Bank,  133 

Sight,  134 

Endowment  Policy,  188 
Equality,  Statement  of,  48 
Equation,  48 
Equator,  253 
Estate,  Real,  192 
Estimating  the  Answer,  38 
Exact  Interest,  100 
Exchange,  128 

Discount  in,  130 

Domestic,  128 

Foreign,  128 

Premium  in,  136 

Rate  of,  135 

Stock,  202 
Exponent,  148 
Express  Money  Order,  130 
Extremes  of  a  Proportion,  142 

Face  of  a  Note,  115 
of  a  Policy,  185,  188 
of  a  Promissory  Note,  245 


Federal  Reserve  Banks,  109,  126 

Flooring,  15 

Forms  of  Indorsement,  112 

Government  Bonds,  208 
Gram,  269 

Great  Circle  of  a  Sphere,  242 
Grocer's  Memorandum,  10 

Hemisphere,  242 

Hexagon,  231 

Hypotenuse  of  a  Right  Triangle,  159 

Index  of  a  Root,  151 

Indirect  Analysis,  38 

Indirect  Tax,  192 

Indorsement,  Forms  of,  112,  246 

Insurance,  185 

Life,  188 

Policy,  185 

Property,  175 
Insured,  the,  188 
Interest,  95 

Compound,  120 

Exact,  100 

On  Mortgage,  198 

Rate  of,  95 

Simple,  95 
Internal  Revenue,  192 

Key,  82 

Lateral  Area  of  a  Cone,  239 

of  a  Cylinder,  170,  235 

of  a  Prism,  232 

of  a  PjTamid,  238 
Lathing,  18 
Ledger,  175,  177 
Legal  Title,  198 
Legs  of  a  Right  Triangle,  159 
Liberty  Loan  Bonds,  107 
Liter,  268      • 
Longitude,  253 
Loss,  77 
Lumber  Measure,  13 

Maker  of  a  Note,  245 
Market  Value  of  Stock,  202 
Maturity,  Day  of,  245 
Means  of  a  Proportion,  142 
Measure,  Lumber,  13 

Volume,  28 

Wood,  28 


INDEX 


285 


Memorandum,  the  Grocer's,  10 
Mercantile  Rule,  251 
Meridian,  253 

Prime,  253 
Meter,  262 

Cubic,  267 

Square,  262 
Money  Order,  Postal,  129 

Express,  130 

Telegraph,  131 
Mortgage,  198 

Interest  on,  198 
Municipal  Bonds,  208 

Xational  Bank,  109 
Negotiable,  246 

Proceeds  of,  115 
Note,  Face  of  a,  115 

Federal  Reserve,  126 

Octagon,  231 

Ordinan.^  Life  Policy,  18S 

Painting.  20 

Papering,  20 

Par  Value,  202 

Parcel  Post,  183 

Partial  Pajinents,  248 

Paving,  26 

Pentagon,  231 

Per  Cent,  58 

Percentage,  61 

Perch,  34 

Personal  Check,  132 

Plastering,  19 

Pohcy,  Insurance,  185,  188 

Face  of,  185 

EndowTnent,  188 
Poll  Tax,  193 
Polygon,  231 
Polygon,  Similar,  231 
Postal  Money  Order,  129 
Powers,  148 

Second,  148 

Third,  148 
Preferred  Shares,  201 
Premium  in  Discount,  136 

in  Insurance.  185,  188 
Price,  the  Selling,  77 

the  Cost,  77 
Principal,  95 


Prism,  231 

Altitude  of,  232 

Lateral  Surface  of,  232 

Total  Surface  of,  232 

Volume  of,  233 
Private  Bank,  109 

Cost  Mark,  82 
Proceeds  of  a  Note,  115 
Profit.  77 
Promissory'  Note,  246 

Face  of,  245 

Maker  of,  245 

Payee  of.  245 
Property,  Personal,  192 

Tax,  192 
Proportion,  142 

Extremes  of  a,  142 

Means  of  a,  142 
Pyramid.  237 

Altitude  of  a,  237 

Lateral  Area  of  a,  238 

Slant  Height  of  a.  237 

Vertex  of  a,  237 

Volume  of  a,  240 

Radius  of  a  Circle,  165 

of  a  Sphere,  242 
Rat-e  in  Exchange.  135 

in  Interest,  95 

in  Percentage,  61 
Ratio,  138 

Sign  of,  13S 

Terms  of  a,  138 
Real  Estate,  192 
Receipts,  182 

Cash,  182 

Rent.  182 

Ser^'ice,  182 
Receipting  a  bill,  9 
Rectangle.  231 
Registered  Bonds.  208 
Revenue,  Internal.  192 
Right  Triangle.  159 

Legs  of  a,  159 

Hypotenuse  of  a,  159 
Roofing,  16 

Tin,  17 
Root.  150 

Cube,  150 

Index  of  a,  151 

Square,  150 


286 


INDEX 


Savings  Bank,  107,  109 
Second  Power,  148 
Section,  260 
Selling  Price,  77 
Series,  Discount,  91 
Services,  Receipt  for,  182 
Shares,  Preferred,  201 

Common,  201 
Shingles,  17 
Sight  Draft,  134 
Slant  Height  of  a  Cone,  237 

of  a  Pyramid,  239 
Slates,  17 
Slip,  Deposit,  110 
Solid,  231 
Sphere,  242 

Diameter  of  a,  242 

Circumference  of  a,  242 

Great  Circle  of  a,  242 

Radius  of  a,  242 

Section  of  a,  260 

Surface  of  a,  243 

Volume  of  a,  244 
Square  Meter,  262 
Stamps,  Thrift,  36 

War  Savings,  36 
Statement  of  Equality,  48 
Stock  Company,  201 

Capital  Stock  of  a,  201 

Certificates  of,  201 

Exchange,  202 

Shares  of,  201 
System,  Metric,  262 

Tariff,  192 
Tax,  192 

Collector,  193 

Direct,  192 

Indirect,  192 

Poll,  193 


Tax  — -  Con. 

Property,  192 

Rate  of,  193 
Telegraph  Money  Order,  130 
Term  of  Discount,  115 
Terms  of  a  Ratio,  138 
Third  Power,  148 
Thrift  Card,  36 

Stamps,  36 
Time,  in  Interest,  95 
Time  Discount,  87 
Tin  Roofing,  17 
Title,  198 

Legal,  198 
Total  Surface  of  a  Cone,  239 

of  a  Cylinder,  235 

of  a  Prism,  233 

of  a  Pyramid,  238 
Township,  260 
Trade  Discount,  87 
Triangle,  231 

Right,  159 

Value,  Par,  202 

Market,  202 
Vertex  of  a  Cone,  239 

of  a  Pyramid,  237 
Vertices  of  a  Square,  161 
Volume  of  a  Cone,  240 

of  a  Cylinder,  170,  236 

of  a  Prism,  234 

of  a  Pyramid,  240 

of  a  Sphere,  244 
Volume  Measure,  28 

War  Savings  Certificates,  36 

Plan,  36 

Stamps,  36 
Wood  Measure,  28 


ANSWERS 

Pages.  — 1.    S11.90.       2.   S40.15. 

Page  9.-3.   S2.15.       4.    3.74. 

Page  10. —1.    S3.51.       2.    S3.95.       3.   $3.49.       4.    $49.85. 

Page  11. —1.   6150.50.       2.   $1909.10. 

Pagel2.  — 3.    $639.       4.    §9.522.50.       5.    84163.25.       6.    S 202.50. 

Page  14. —  1.   12.       2.    14.       3.    10.       4.    llf.       5.    9.  6.    llf        7.    8. 

8.  10|.  9.  6|.  10.  2i.  11.  3.  12.  4.  13.  6.  14.  3^.  15.  7. 
18.  9|.  17.  10.  18.  lOf.  19.  10.  20.  12.^.  21.  13^.  22.  15. 
23.  15.  24.  18.  25.  20.  26.  15.  27.  25.  28.  30.  29.  15.  30.  20. 
31.  20.  32.  24.  33.  14.  34.  21.  35.  9f  36.  IT^.  37.  imj. 
38.  315.  39.  500.  40.  384.  41.  201A.  42.  400".  43.  810. 
44.   $72.48. 

Page  15.— 45.    $135.98.       46.    $92.05. 

Page  16. —1.  210.  2.  225.  3.  320.  4.  234f  5.  253J.  6.  290. 
7.    16U^.       8.    255j\.       9.    307^V       10.   .$12.96.       11.   S  16.13.       12.   $12.96. 

13.  $8"l0.      14.  $12.67.     15.  $16.51.      16.  89.45.      17.  $13.02.      18.  S18.12. 

Page  17. — 1.  26  bunches.  2.  33  bunches.  3.  41  bunches.  4.  47 
bunches.       5.  51  bunches.       6.  47  bunches.       7.  33  bunches.       8.  47  bunches. 

9.  81  bunches.       10.    $15.46.       11.    S27.42.       12.    $34.54.       13.    $166.50. 

Page  18.  — 14.    8150.11 

Page  19. -1.   9  bundles.       2.    $6.30.      3.  $9.80. 

Page  20.  —1.  16  sq.  yd.  2.  23i  sq.  yd.  3.  21i  sq.  yd.  4.  24?  sq.  yd. 
5.  28|sq.  yd.  6.  34  sq.  yd.  7.  i4  sq.  yd.  8.  20|f  sq.  yd.  9.  22^f  sq. 
yd.       10.   31xV  sq.  yd.       11.  40i|  sq.  yd.       12.   49^;  sq.  yd.       13.    lUq  sq.  yd. 

14.  13|j  sq.  yd.  15.  20/^  sq.  yd.  16.  28|  sq.  yd.  17.  39y^j-  sq.  yd. 
18.  56/.  sq.  yd.  19.  $19.25.  20.  826.95.  21.  826.25.  22.  828. 
23.  830.80.  24.  $35.35.  25.  $44.10.  26.  850.40.  27.  $59.85. 
28.   $71.7.5.       29.    $16.80.       30.    $41.65.       31.    $52.80. 

Page  21. —1.    .72  gal.  2.    .896  2:al.  3.    1.08  gal.  4.    1.28  gal. 

5.    1.584  gal.  6.    1.748  gal.  7.    2.56  gal.  8.   5.4  gal.  9.    8.4  gal. 

10.  $56.80.  11.    $14.40.  12.    $18.67.  13.    8  28.80.  14.    859.12. 

15.  $100.  16.  825.56.  17.  $31.67.  18.  $38.  19.  $48.67. 
20.  $60.78.  21.  $110.22.  22.  $1.08.  23.  81.35  24.  $1.52. 
25.  $1.62.  26.  $1.80.  27.  $1.92.  28.  $2.38.  29.  8  2.70. 
30.  $3.17. 

Page22.  — 31.    $23.04.  32.   823.04.  33.    825.60.  34.    $36.87. 

36.   i§72.54.       36.    $249.60.      38.   $61.61.       39.    $199.22. 

287 


288 


ANSWERS 


Page  23. 

8  rolls. 


1.    10  rolls. 


2.    10  rolls. 


3.    Walls,  12  rolls.     Ceiling, 


Page24.  —  4.    $4.50.       5.    $5.25.       6.    $14.40. 


6. 
12. 
17. 
22. 


Page  25. 

40  yd.       ' 
32  yd. 

53i  yd. 
$57.63. 


■1.    20  yd.        2.    30  yd.        3.   24  yd. 
20-^  yd.        8.   361  yd.        9.    38|  yd. 

13.    32  yd.  14.    49  yd.  15. 

18.    65iyd.  19.    $44.80.  20. 

23.    $51.20.  24    $69.34.  25. 


4.    211yd. 
10.    28  yd. 
65  yd. 
$42.67. 

$181.13. 


5.  281yd. 

11.  40  yd. 
16.  29|yd. 
21.  $43.63. 
26.    $90.75. 


27.    $131.25.      28.    $176.      29.    $22.80.      30.    31yd.     31.    Lengthwise,  $85.69. 


Page  26. —1.   $56.         2.    $105. 
6.    $560.        7.    $63.         8.    $141.75. 
12.    $412.42.        13.    $183.75.        14. 
17.    $1066.67.  18.    $1280.  19. 

22.    $9000.       23.    $13,333.34.       24. 
27.   $1600.       28.    $3110.40. 


3.    $117.60.         4.    $252.        5.    $315. 

9.    $189.        10.    $52.50.        11.   $448. 

$4.36.80.        15.   $268.80.        16.    $793.80. 

$.3333.34.  20.   $4000.         21.   $8400. 

$24,000.       25.   $42,240.       26.   $140,800. 


Page  27.- 
33.    $10,240. 
38.    $42,240. 
43.    76  sq.  yd. 

Page  28.  - 

5.    21  cords. 
10.   9|i  cords. 
15.    1|  cords. 
20.    2yL  cords. 

Page  29.  - 

1.    28|  bu. 


•29.    $768.  30.    $1228.80. 

34.    $67,-584.        35.    $16,896. 
39.    $76,032.         40.    $84,480. 
44.    325  sq.  yd.       45.    $  288. 


3| 


6. 
11 


1728  bu. 
36O2V  bu. 


1.   2  cords.  2. 

6.  3f  cords.         7. 

11.  10  cords.         12. 
16.    If-  cords.  17. 

21.    3  cords.        22. 

•25.    $12.66.  26, 
2.    96  bu. 

7.  140f  bu.  8. 

12.  1159fbu. 


cords, 
cords. 
18  cords. 


cords. 
4^  cords. 


■  2? 


51 


>^  cords. 
3.    128  bu. 

70i  bu. 


31.    $2048. 
36.    $1.5,840. 
41.    $214.63. 

3.   3  cords. 
8.    5f  cords. 

13.    1  cord. 
18.    1^  cords. 
23.    6^  cords. 

4.    288  bu. 
9.    105^V'bu. 


32.   $5120. 

37.    $38,016. 

42.   $1.75. 


4.    2|  cords. 

9.   7 1  cords. 

14.    I  cord. 

19.    1^  cords. 

24.    6  cords. 


5.    864  bu. 
10.    3031^  bu. 


Page  30.  — 13.    312i  cu.  ft 
cu.  ft.         17. 
cu.  ft.         21. 

cu.  ft. 


812^  cu.  ft. 
1875  cu.  ft. 


14.    375  cu.  ft. 
18.    1125  cu.  ft. 
22.    3125  cu.  ft. 


15.    6621  cu.  ft. 
19.    1250  cu.  ft. 
23.    3750  cu.  ft. 


IG.   650 

20.    1562^ 

24.    9000 


1.    $57.60. 
6.    $145.35. 
11.    $201.88. 
18.   $15. 
21.    $52.74. 


2.   $66.67. 
7.   $190.  8. 

12.    $469.24. 
17.    $10.56.  18 


3.    $84. 
$456. 
13.    $7.50. 
$  1848. 


4.    $112.50. 
$162.-56. 

14.   $6.40. 
19.    $352. 


5.    $108. 

10.    $187.47. 

15.    $13. 

20.    $34.67. 


Page  32.  — 1. 

4.    14,850  bricks. 
8.    16,500  bricks. 
12.    3600  bricks. 
16.    7020  bricks. 


7920  bricks.  2. 

5.    17,600  bricks. 
9.    17,600  bricks. 
13. 


06IO  bricks. 


17.    8700  bricks. 


7700  bricks. 
6.    9900  bricks. 
10.   29,700  bricks. 

14.    4200  bricks. 
18.   9450  bricks. 


20.    10,080  bricks.         21.    $68.64. 


3.    11,880  bricks. 

7.    8800  bricks; 

11.    2520  bricks. 

15.   6000  bricks. 

19.    19,947  bricks. 


Page  33.  — 1.    $300. 

5.    $229.17. 

Page  34.-6.   $205..56. 
10.   66|cu.  yd.       11.    $211.86. 


2.   $397.50. 

7.   $103.68. 
12.   200  ;  400 


3.    $406.67. 


4.   $667.50. 


8.   $14.89.  9.   $78.76. 

800.       13.    $325.37. 


ANSWERS  289 

Page  35.  —  1.  8  perches.      2.  27  perches.      3.  30  perches.       4.  66  perches. 

5.  44  perches.  6.  104  perches.  7.  67  perches.  8.  94  perches.  9.  99 
perches.  10.  142  perches.  11.  97  perches.  12.  117  perches.  13.  10.24 
perches.       14.    ^20.67. 

Page  37. —1.  $20.85.       2.  $100.32.       3.  $84.       4.  $316.50.      5.  $16.40. 

6.  $47.40.       7.    $63;  $12. 

Page  43. —1.    $630.  2.    45 1?.  3.    f  4.    40  yd.  5.    88  yd 

6.  $233.50.       7.    $6.75.       8.    }.       9.    $20. 

Page  44. —  10.  $60.  11.  $1800.  12.  13  1b.  13.  §7.50.  14.  $3.30. 
15.  $4.  16.  $26.60.  17.  $1.96  each;  $4.92.  18.  $22  gain.  19.  $624 
gain.      20.    f^,  ^%. 

Page  45.— 21.  $1.50.  22.  2  doz.  23.  32^.  24.  48|  lb.  25.  76}fj?. 
26.  $17.50.       27.  $3.84.       28.  lo^^g  ^.      29.  $4.50.      30.  $11.10.      31.  $4.75.' 

Page  46.— 32.  10 j?.  33.  $680.  34.  $9  cheaper  to  rent.  35.  $293.60. 
36.  56/yqt.  37.  24  cows.  38.  900  bu.  39.  25  A.  40.  1st,  50)?;  2d,  60)?. 
41.    $6800;  $100  per  A. 

Page  47.-42.  4  bbl.  43.  100  cu.  ft.  cement ;  200  cu.  ft.  sand  ;  400  cu. 
ft.  gravel.  44.  60  da.  45.  $384.  46.  94  bii.  47.  40  cu.  ft.  cement : 
80  cu.  ft.  sand  ;  160  cu.  ft.  gravel.       48.    $99.       49.    $31.95. 

Page  51.— 1.  4.       2.  3.       3.  1.       4.  4.       5.  4.       6.  10.       7.  12.  8.  11. 

9.    17.       10.    5.  11.    8.       12.  5.       13.  6.  14.  3.       15.  7.       16.  |.  17.  |. 

18.    V-        19-   3.        20.    2.        21.    3.        22.  5.  23.   4.        24.    2.  25.    V- 

26.  V-       27.    3.       28.    s^. 

Page  53. —1.   16.       2.    16.        3.    12.       4.    $25.       5.   30  cai-s.        6.    S18. 

7.  330  ft. 

Page54.  —  8.  85.  9.  108.  10.  114.  11.  140.  12.  43^.  13.  36^. 
14.    $850.       15.    85  cans.       16.    16  yr.       17.    145  1b.       18.    $56;  $80. 

Page  55.  — 19.   25,75.       20.    10,50.       21.    6yr.,  18vr.     22.    12yr.,  36yr. 

23.  601b.,  1801b.      24.  20,40.      25.  $3,  $12.      26.  AVagon,  $50;  Horse,  S 200. 

Page  56.  — 27.  Lot,  8 500  ;  House,  $ 2500.  28.  5.  29.  15.  30.  15. 
31.  10.  32.  7.  33.  12.  34.  10,40.  35.  $3.  36.  5  boys.  37.  $40. 
38.   $5. 

Page  57. —39.    $1200.  40.   Harry,    20  (^  ;    Tom,    35  J?  ;    Jack,    45  ^ 

41.  Jerry,  57^  lb.;  his  father,  192^  lb.  42.  Kate,  4  ;  Emily,  12  ;  Mary,  36. 
43.    Dick,  $10  ;  Earl,  818.  44^  Truck,  2450  lb.;  coal,  4900  lb.,  or  2^%  T. 

45.   Bv  boat,  40  mi.;  by  rail,  120  mi.  46.   Repairs,  $25;  gasoline,  $150. 

47.   Food,  $  1000  ;  rent,  $  500.       48.    Sister,  6  yr. ;  boy,  12  yr. ;  father,  36  yr. 

Page62.— 1.   4,  5.6,  4.5,  11.25.        2.4.8,7.6,11,19.2.       3.5.4,9.81,15, 

27.  4.  0.3,13,21,41.25.  5.  $41.25.  6.  $45.  7.  $57.60.  8.  $68. 
9.  $31.38.  10.  $91.21.  11.  $183.15.  12.  $234.76.  13.  8500. 
14.  $900.  15.  $1612.50.  16.  $3000.  17.  $100,  $200,  $400,  $800. 
18.  $187.50,  S 375,  $562.50,  $750.  19.  S 800,  $  1600,  $2096.  20.  S150, 
$200,  $400,  $2000.           21.    $550,  $625,  $900.          22.    $5,  $250.  23.    .1. 

24.  .15.  25.  .05.  26.  .1.  27.  .1.  28.  .9.  29.  4.5.  30.  2.5, 
31.    1.6.       32.    1.5.       33.    4.       34.    4. 

1.   6  boys.      2.   $400.       3.   $437.50.      4.   S760o 


290  ANSWERS 

Page  63.-5.  $1.12^.       6.  .$3600.       7.  $24.       8.  1020  gal.      9.   180  men, 

270  women,  90  children.     10.  $2800.       11.  $4884.08.  13.  Real  estate,  $8100; 

bonds,  $18,000;  business,  $21,600;  savings  bank,  $6300.  13.  $480. 
14.    $4500. 

Page  65.  —  1.    20  9fc,  33^ ^o,  25  %,  20  fo.  2.    12|  ^G,  20 fo,  50  %,  20  7c. 

3.  20  7o,  26f  ^0,  40  fo,  55f  %.  4.  40  %,  60  ^o,  80  %,  100  fo.  6.  6^  ^o,  8^  %, 
5%,  50%.  6.    20  fo,  20%,  20%,  20%.  7.   331%,  6|  %,  25%,  1  %. 

8.  5  %,  2  %,  2  %,  .2  %.  9.  40  %,  60%,  75  %,  30  %.  10.  48.1  %,  40  %, 
28.6%,  29.6%.  11.  42.9%,  41.3%,  35.2%,  46.3%.  12.  28.1  %,  34.8  %, 
25.7  %,  48.8  %.  13.  22.8  %,  30.5  %,  33.6  %,  36.7  %.  14.  28.2  %,  29.2  %, 
36.6  %,  35  %.  15.  44  %,  42.7  %.  18.9  %,  19  %.  16.  31.9  %,  28.1  %,  21.5  %. 
17.   6.5%,  43.3%,  7.9%. 

1.   60%.       2.   831%.       3.   20%.       4.   25%. 

Page66.  — 5.    $40;  25%.  6.    20%.  7.    75%.  8.   85^%. 

9.  16|%.  10.  14f%.  11.  House,  $5200;  lot,  $2800.  12.  3.94%. 
13.   166|  %.        14.    5  %.        15.    65  %  ;  65  cents  on  the  dollar.         16.   30  %. 

Page  67.  — 17.  360  mi.  18.  41f  %  in  5  days  ;  25  %  in  3  days  ;  58^  %  in 
7  days;  91 1  %  in  11  days.  19.  66|%.  20.  16f%  to  individuals  ;  33^% 
to  hotels  ;  50  %  to  grocers.  21.   Lot,  25  %  of  house  ;  house,  80  %  of  total. 

22.  60%.  23.  4.581%.  24.  Crescents,  34,  70.58%  ;  Stars,  36,  69.44%  ; 
Imperials,  33,  60.6  %  ;  Orioles,  34,  76.47  %. 

Page  69.-1.   200,  150,  250,  250.  2.    300,  200,  166|,  200.  3.  200, 

160,  280,  350.  4.    150,  300,  300,  384.  6.    125,  120,  180,  288.  6.  400, 

225,  200,  160.         7.    200,  148/^,  200,  200.         8.    225,  200,  300,  208f  9.  120, 

208^,  200,  125.       10.    80,  200,  175,  137|.  11.    200,  200,  200,  175. 

1.   60  boys.  2.    1251b.  3.    $4000.  4.   300  miles.  6.   6. 

6.    1400  bu.  ;  980  bu.       7.    Cost.  $166.67  ;  Profit,  $33.33  ;  20  %. 

Page  70.— 8.   $1536;  37^%.        9.    128  ;  80.        10.    $1500.       11.    $4000. 

Page  71.-1.    1.56.           2.   2.19.           3.   2.81.  4.    3.44.  5.   4.06. 

6.    4.69.       7.    4.17.        8.    6.25.       9.    7.5.        10.   8.75.  11.   9.58.  12.    10.42. 

13.    9.38.        14.    11.25.        15.    13.13.       16.    14.38.  17.    16.25.  18.   18.13. 

19.   8.33.          20.    12.5.          21.    14.17.         32.    15.  23.    15.83.  24.    17.5. 

35.    16.67.       36.   23.33.       37.   26.67.        28.   31.67.  29.   36.67.  30.   38.33. 

31.    46.88.        33.   56.25.       33.    65.63.       34.    71.88.  35.    81.25.  36.    90.63. 

37.    50.          38.    54.17.          39.    58.33.          40.    62.5.  41.    66.67.  43.    75. 

43.   79.17.        44.   87.5.        45.    91.88.        46.    96.25.  47.   105.  48.    109.38. 

49.    113.75.           50.    118.13.            51.    122.5.           53.  $52.50.  53.   $82.50. 

54.  $103.50.  55.  $120.  56.  $48.60.  57.  $70.19.  58.  $78.13. 
59.    $26.56. 

Page  72.— 60.   $137.50.  61.    $156.25.         62.   $16.28.  63.   $22.28. 

64.    $40.37.         65.   $39.94.  66.    $57.09.         67.    $172.56.  68.    $223.44. 

69.    $264.06.      70.    $.25.      71.  $.37^.      72.    $.50.      73.    $2.00.  74.   $3.00. 

75.   $3.77.           76.    $11.25.           77.   $22.50.           78.   $75.00.  79.    $200. 

80.    10%.       81.    lli%.        83.  20%.       83.   20%.        84.   20%.  85.    20%. 

86.   20.2+%.              87.    20%.             88.   20%.             89.    30%.  90.   25%. 

91.    13.8+%.          93.    12^%.  93.    10%.          94.    10.8+%.  95.   10.7+%. 

96.    12.2+%.           97.    13%.  98.    12^%.           99.    15.6+%.  100.    25%. 

101.    20%.           102.   20%.  103.   18%.           104.    12*  %.  105.    10%. 


no. 

280. 

116. 

419. 

121. 

.004. 

126. 

S  96. 

ANSWERS  291 

106.  IGf'T'c.         107.   42.8+ fo.  108.    33^%.          109.    45.4+%. 

111.  325.         112.   500.          113.  480.         114.    125.         115.    62.4. 

117.  563.12^.              118.    .6.  119.    .02.              120.    .312. 

122.  815.625.          123.    §27.50.  124.    8  28.          125.    •S22..50. 

127.  8  80.          128.    893.75.  129.    81350.          130.   81125.          131.    81000. 

Page  73.  — 1.    §20,000.         2.   2%.        3.   46j7c.        4.    8322.        5.    5%. 

6.  25  7c  of  cost  price;  20%  of  selling  price.  7.  Marked  price,  $375; 
Selling  price,  8300;  Cost  price,  8250.             8.    82000. 

Page  74.-9.    8  47.25;   8  .33|.  10.    1250  A  ;   325  A.  11.    8.04^; 

8.05.       12.    33|%.  13.    81687.50  ;  93|%.         14.    83125.  15.    8  57.000. 

16.    83570;  8 570  profit.       17.    15|&j  %  ;  2f|  %. 

Page75.  — 18.  8889.      19.  2100  bii.      20.  20|fc.      21.  18;.       22.  120%. 

23.  8142.95.       24.  30.9+%.       25.  60%,  25%,  15%.     26.   120  lb.,  50  lb.,  30  lb. 

Page  76.  — 27.    816.  28.   601b.  29.   148  1b.  30.   The  latter. 

31.    94.5  1b.       32.    39.6  1b.       33.    30.411b.       34.    $173.25. 

Page  79. —1.84.       2.   §6.       3.    8*7. 80.       4.    811.25.       5.  818.       6.  819. 

7.  812.50.        8.   820|.       9.    822.50.       10.    $40.       11.    841.25.       12.    8  87.50. 

13.  86.27^.  14.  819.22.  16.  825.25.  16.  8562.50.  17.  83200. 
18.  88750.       19.    8115.       20.    8150.       21.    8150.80.       22.    8200.       23.    8228. 

24.  8230.  25.  8220.  26.  8287.50.  27.  8337.50.  28.  8466.67. 
29.  8540.  30.  §937.50.  31.  8274.96.  32.  $431.48.  33.  8523.19. 
34.  §696.73.  35.  §9000.  36.  817,000.  37.  S50.  38.  §90.  39.  8112.50. 
40.  8180.  41.  §231.25.  42.  8292.50.  43.  8127.55.  44.  8306.34. 
45.  §595.88.  46.  $685.13.  47.  88583..S3.  48.  810,342.50.  49.  81020. 
50.  §1312.50.  51.  §1487.50.  52.  82125.  63.  83187.50.  64.  83400. 
55.  §1125.45.  56.  §1728.56.  57.  §1881.95.  58.  §3123.92.  59.  84666.93. 
60.  $5210.63. 

Page  80.  — 1.    §750.       2.    S1041|.       3.    §1666f.       4.   §4000.       5.    §3750. 
6.   §600.       7.    §600.       8.    §1000.      9.    81000.       10.    8 1500. 

Page  82. —  1.   33^%.         2.    20%.         3.    10%.         4.   15%.  6.   33^%. 

6.  33i%.  7.  10%.  8.  20%.  9.  11|%.  10.  16|%.  11.  25%. 
12.   16|%. 

1.   nil.         2.   rel.         3.    ril.      4.    rml.        5.   ram.         6.    dum.  7.    dml. 

8.  rmlx.        9.   rtnm.         10.    uxml.         11.    umtx.        12.    dulx.  13.    muml. 

14.  etnm. 

Page  83.  — 1.    8360.         2.    1U%.         3.    82400.         4.   8.60.         5.    $700. 
6.    843.70.  7.   88  loss;  4%.  8.    827.20.  9.    84.80.  10.    27|%. 

11.   §.54.       12.    §60. 

Page84.  — 13.   85.       14.  8^%.       15.  886.25.       16.  85  loss.       17.  100%, 
82.25.       18.    82100  gain;  20%.       19.    §3750,  §5625,  8375  loss. 

Page 86.— 1.  8128.21.      2.  8138.89.      3.  8198.41.      4.  8375.       5.  81000. 

6.  81855.65.      7.  §2977.62.       8.  83525.64.       9.   814.486.98.       10.  837,692.31. 

11.  §2131.94.       12.    8  4369.09.       13.    8  5769.23. 

Page88.  — 815.       2.    §12.50.       3.  §30.      4.  $37.50.      5.  §78.      6.  S150. 

7.  §27.55.  8.    §44.28.  9.    862.54.  10.    §155.30.  11.    8157.73. 

12.  §258.47.  13.    §24.75.  14.    839.01.         15.    884.66.  16.    892.08. 


292  ANSWERS 

17.  $131.90.         18.    1203.03.         19.    $47.69.  20.    $64.51.  21.    $88.40. 

22.  $187.87.       23.    $235.56.       24.    $375.27. 

1.    $4.80.       2.    $19.20.       3.   20^^.       4.   209^o.       5.    $405.       6*.    $152. 

Page  89.  — 7.    $135.        8.    10%.       9.   $2.08.        10.    $446.39.        11.   $28. 
12.   $80.       13.    $918.75.       14.   $266.67.       15.    $1460.       16.   No  profit. 

Page90.  — 17.    $.05  per  cake,  100%  gain.  18.    $2.75.  19.   $40. 

20.    $800.        21.    $112.50.        22.    $3375,  $9618.75.        23.  $140.       24.  $2460. 

Page  91.— 1.   $64.13.         2.   $76.95.  3.    $72.         4.    $85.         5.   $90. 

6.    $254.36.       7.   $314.64.       8.    $402.04.       9.    $575.91.       10.    $513. 

Page  92. —  1.    $432.        2.    $146.88.        3.   38|%.         4.    $4.61.         5.    1st 
$.221  better.       6.    $69.90.        7.    The  same.        8.    25%.       9.   2d  $ 6.39  better. 

10.  $81.       11.    Agent's  gain,  $26.60;  Amount  paid,  $216.60. 

Page  94. —1.    $477.94.  2.   $746.90.  3.    $3420.  4.    $686.35. 

5.  $692.52. 

Page  96.— 1.    $200.       2.    $216.       3.    $393.75.       4.    $18.83.       5.  $45.15. 

6.  $98.77.  7.  $105.  8.  $  136.. 50.  9.  $406.  10.  $22.63.  11.  $413.50. 
12.    $149.17.       13.   $30.50. 

Page97.  —  14.    $83.63.         15.    $142.20.         16.    $88.09,         17.    $248.95. 

18.  $252.50.       19.    $547.92. 

Page  98.  — 1.    $22.05.  2.    $37.80.       3.    $65.07.       4.    $36.  5.    $74.41. 

6.   $80.96.          7.    $136.86.          8.    $189.99.          9.    $241.53.  10.    $239.41. 

11.  $810.94.  12.  $90.68.  13.  $17.50.  14.  $50.63.  15.  $65.50. 
16.    $18.73.       17.    $62.49.  18.    $136.05.       19.   $289.85. 

Page  99.-20.    $170.      21.    $144.50.       22.    $1087.20. 

Page  100. —1.   $137.30.     •     2.    $171.08.  3.    $227.24.         4.   $282.14. 

5.  $.300.40.  6.    $361.40.  7.    $428.08.  8.    $497.46.  9.   $272.75. 

10.  $285.97.  11.  $383.42.  12.  $478.92.  13.  $373.52.  14.  $448.49. 
15.  $499.46.  16.  $632.56.  17.  $48.72.  18.  $54.36.  19.  $51.57. 
20.  $63.90.  21.  $110.55.  22.  $227.70.  23.  $399.74.  24.  $468.59. 
25.  $99.17.  26.  $333.11.  27.  $306.14.  28.  $459.15.  29,  $679.38. 
30.  $561.47.  31.    $695.61.  32.    $816.93. 

Page  101.  — 1.    $1.32.       2.   $1.66.       3.    $3.05.       4.   $3.25.  5.    $4.02. 

6.  $5.72.       7.   $.6.01.       8.    $6.70.       9.    $12.43.       10.    $23.59.  11.    $2.55. 

12.  $7.51.  13.  $5.26.  14.  $3.32.  15.  $7.11.  16.  $9.32.  17.  $6.56. 
18.    $8.02.           19.    $8.79.           20.   $10.91.           21.    $17.92.  22.    $28.62. 

23.  $37.83.  24.  $12.33.  25.  $20.68.  26.  $45.04.  27.  $32.36. 
28.    $61.29. 

Page  102.— 1.    $2.20.      2.    $3.27.      3.    $8.00.       4.   $13.05.      5.    $19.79. 
6.   $16.13.  7.    $42.24.  8.    $39.05.  9.    $39.50.  10.    $47.58. 

11.  $77.81.       12.    $13.93.       13.    $15.63.       14.    $54.08.       15.    $103.42. 

Page  104.-1.    $18.         2.    $49.50.        3.   $72.         4.    $110.         5.   $210. 
R.   $69.75.  7.    $106.77.  8.    $166.25.  9.    $169.13.  10.    $181.25. 

11.  $149.72.  12.  $494.40.  13.  $729.53.  14.  $784.74.  15.  $1247.38. 
1«.    $18.       17.    $26.3.3.       18.    $251.67.       19.    $15.       20.    $1048.06. 

Page  106.  — 1.    $208.08.       2.    $364.20.       3.    $406.04.       4.    $624.18. 


ANSWERS  293 

Page  108. —  1.    $35.  2.   $148.75.  3.    $32.  4.   $817.50. 

5.  $106,232,939.76.      6.    $674.49.       7.    $474,636,463.63. 

Page  111. —1.    $458.40.        2.   $604.42.        3.    $1096.20.         4.    $1072.17. 

6.  $2436.90.       6.   $6374.97.       7.    $1180.30. 

Page  113. —1.    $442.75.        2.   $1296.26. 

Page  114.— 3.   $3600.33.  4.   $8018.30.  5.    Men.    $2670,    Tues. 

$3236.03,  Wed.  $1790.93,  Thurs.  $2885.26.  6.    $1328.71.  7.    $1273.87. 

Page  115. —1.  $1.60,  $298.60.  2.  $3.60,  $346.50.  3.  $4.50.  $445.50. 
4.  $7.19,  $567.81.  5.  $7.60,  $742.50.  6.  $5,  $995.  7.  $12.50, 

$1487.50.       8.   $33.75,  $2216.25.       9.    $31.25,  $2468.75.       10.   $30,  $2970. 

Page  116.— 5.    $2479.17.       6.    $2975.       7.    $4468.75. 

Page  117.*  — 1.  April  30,  60  days,  $9.86,  $990.14.  2.  June  19,  60  days, 
$9.04,  $  1090.96.  3.  June  8,  60  days,  $  .83,  $  100.65.  4.  March  2,  60  days, 
$8.29,  $999.93. 

Page  118.*  — 5.  April  9,  24  days,  $3.96,  $1200.97.  6.  60  days,  $14.98, 
$1503.51.  7.    60  days,  $16.68,  $2012.91.  8.   July  31,  46  days,  $7.62, 

$1202.24.         9.    $250.91.         10.    $452.65. 


Page  119. 

5.    $2030.46. 

1.    $300. 
6.    $2016.81. 

2.    $1500. 
7.    $1224.49. 

3.    $500. 
8.    $20,227.56. 

4.    $651.64. 
9.    $3563.29. 

Page  121. 
5.    $393.71. 
10.    $155.36. 

I.  $76.41. 
6.    $47.19. 

II.  $92.73. 

2.   $78.81. 

7.   $70.77. 

12.    $465.34. 

3.   $101.92. 
8.   $102.93. 

4.    $338.23. 
9.   $81.68. 

Page  123. 
6.   $435.94. 

1.    $272.10. 

2.    $345.27. 

3.    $462.28. 

4.   $349.15. 

Page  124. 
10.    $50.07. 

6.   $333.09. 
11.    $87.72. 

7.    $529.75. 
12.    $170.63. 

8.   $504.03. 
13.    $114.75. 

9.    $638.76. 

Page  125.— 1.    $533.50.         2.   $831.44.        3.    $764.70. 

Page  127. —  1.    $48,000,000.      2.    40,000  shares.      3.    $  1,320,000  of  stock. 

Pagel28.  — 4.    $4,684,000.         5.    $200,000.         6.   $6,894,994  ;  58+%. 

Page  130. —1.   $  .06  difference.  2.    $.65.  3.   $  .08  difference. 

4.  $1.52,  $.24. 

Page  136.  — 1.   $2000.40.       2.   $1999.60.       3.    $3000.90.       4.    $4997.60. 

5.  $4003.  6.   $1006.  7.    $1488.76.  8.    $1996.  9.   $3496.50. 
10.    $6991.         11.   $4488.76. 

Page  137. —12.    $3022.50.  13.   $4003.50.  14.    $3998. 

15.   $4477.60.      16.    $1.50.       17.   $10,005.       18.    $9514.68.       19.   $10,630.26. 
20.    $8,258.81,  $41.19. 

Page  139.-1.   I  2,  |,  2,  |.  2.  f,  h  |,  i  |.  3.   2,  f,  |,  |,  f 

4.   4,-V,/,  h  I      5.    hj^h\h  h    ^6.    I  f,  f,  h  if      7.   I,  I,  il,  f,  f. 

®*    71    f»    6»    iJ5'>   5*  9'     ?»    ^?    TUi  ^^'    10- 

•  Interest  calculated  by  the  Exact  Method  (p.  100). 


294  ANSWERS 

Page  140.  — 1.    9,27.       2.    20,25.       3.   3.5,40.       4.   40,70.       5.    42,98 

6.  61t^.  113/^.       7.    36,  114.        8.   70,  130.        9.    64,  144.        10.   93^^,  170^f 

11.    lllf  ^-,  212/^.         12.    146H,  353|f 
1.   3  to  2.        2.    5  to  1.         3.   7  to  27. 

Page  141.— 4.    525  1b.  5.    1562|  lb.  6.   $18;|42.  7.  13|^  lb. 

8.  12000,  $2800.       9.  Child,  $10,714.29;  widow,  $26,785.71.       10.  $18,  $12. 

Page  143.— 1.   3.       2.   2.       3.    15.       4.   27.       5.   8.       6.    13^.       7.   10. 
8.    1.       9.   ^|.       10.    7.       11.    I.       12.    .04.       13.    .02.       14.    3. 

Page  145.  — 1.    $27.          2.  $35.          3.    $60.  4.   $160.  5.    $38.40. 

.6.    $135.             7.    $159.50.  8.   $140.            9.  $157.50.  10.    $637.50. 

11.    $419.75.           12.    $680.40.  13.   $27.30.  14.   $528.  15.   40  mi. 

16.    $10.56.       17.   $6.57.       18.  38  1b. 

Pagel46.  — 19.    11,000.  20.   $3.20.  21.   $86.40.  22.  6f  days. 

23.  371  lb.,  27  lb.  24.  8  days.  25.  6  days.  26.  39  days.  27.  48 
women.         28.   108  days. 

Page  147.  — 29.   6 ^  days.       30.    27  J'^  days.       31.    15  day.s.       32.   60  more. 
33.    117^  days.       34.   80  days.       35.    3  men.       36.  38  men.     37.    54  men. 

Page  150.  — 1.    676.      2.   1225.      3.    1764.       4.   2916.       5.    4225.      6.225. 

7.  441.  8.  625.  9.  900.  10.  2025.  11.  i.  12.  |.  13.  ||.  14.  ji^. 
16.  -sVo.  16.  6.25.  17.  9.9225.  18.  64.481201.  19.  4.6225. 
20.   34.328125.             21.    225  sq.  in.             22.    576  sq.  in.             23.   900  sq.  ft. 

24.  1225  sq.  ft.  25.  1764  sq.  ft.  26.  2500  sq.  ft.  27.  2500  sq.  yd. 
28.  2500  sq.  rd.  29.  4225  sq.  yd.  30.  5625  sq.  rd.  31.  110.25  sq.  ft. 
32.  232.6625  sq.  ft.  33.  348|  sq.  ft.  34.  420.25  sq.  ft.  35.  588.0625  sq.  ft. 
36.  106^  sq.  yd.  37.  160*  sq.  yd.  38.  2351  sq.  yd.  39.  348|  sq.  yd. 
40.  427 1  sq.  yd.           41.    216  cu.  in.  42.    1000  cu.  in.  43.    4096  cu.  in. 

44.  729'cu.  ft.  45.  1728  cu.  ft.  46.  8000  cu.  ft.  47.  3f  cu.  f t. 
48.  1 .953125  cu.  ft.  49.  15f  cu.  ft.  50.  42|  cu.  ft.  51.  190/^  cu.  ft. 
52.    614^  cu.  ft. 

Pagel51.  —  I.    15.       2.    18.       3.  24.  4.  27.  5.  28.       6.  31.       7.  32. 

8.  33.  9.  35.  10.  36.  11.  42.  12.  45.  13.  48.  14.  50.  15.  56. 
16.  64.  17.  22  ft.  18.  26  ft.  19.  30  ft.  20.  31ft.  21.  81ft. 
22.   84  ft.       23.    9071  ft.       24.    1056  ft. 

Page  154. —1.  34.       2.  35.       3.  43.      4.   39.       6.   44.       6.  42.  7.  45. 

8.    51.       9.    54.       10.   41.  11.    56.        12.    59.       13.   57.        14.    6Q.  15.   64. 

16.  09.  17.  74.  18.  72.  19.  79.  20.  88.  21.  86.  22.  93.  23.  97. 
24.   96.       25.    98. 

Pagel55.  —  26.    121.          27.  135.          2fr.    127.          29.    124.          30.  138. 

31.    151.       32.    147.       33.   158.  34.    175.       35.    172.       36.    181.       37.  196. 

38.    203.       39.    208.       40.    302.  41.    305.        42.   309.        43.    321.       44.  353. 

45.  388.  46.  486.  47.  577.  48.  647.  49.  773.  50.  888.  51.  899. 
52.    979.       53.    5210.     54.   6970.  55.    5121.       56.    8005.       57.    9015. 

Page  157. —1.    5.14.       2.  51.4.       3.  .514.       4.64.7.      5.  .696.       6.  .036. 
7.    .027.        8.   54.8  9.    -0847.  10.   .0181.  11.   70.31.  12.    9.807. 

13.  .0177.  14.  .0057.  15.  600.3.  16.  80.02.  17.  12.247+.  18.  18.027+. 
19.  23.874+.  20.  28.124+.  21.  34641+.  22.  132.287+.  23.  188.175+. 
24.   255.180+.       25.   352.641+.       26.   456.146+        27.    12.414+.        28.   58.794+. 


ANSWERS 


295 


29. 
35. 

6. 
11 

6. 
11 


.433+       30.    .013+.       31.   .715+        32.   25.988+.       33.    .816+.       34.    .774+. 
.845+.      36.    .935+.      37.    .957+.      38.    .888+.      39.    .887+.       40.    .850+. 


ihr. 


68  ft. 
7. 


Page  158.  —  1 
60  ft.        6       " 

31  boys. 

Page  160.  — 1.   20  m. 

13  ft.  7.  26  rd. 


2.    24  in.  3. 

§625.        8.    240  rd. 


208.710+  ft. 
9.    $4800. 


8 


2.   25  in. 

18.439+  ft. 


3.   30  ft.  4. 

9.    33.54+ ft. 


4. 
10. 

40  ft. 
10. 


1669.68+  ft. 
122.474+  ft. 


5.  80  ft. 
39.051+  ft. 


90.138+ ft.   12.  109.658+ ft.   13.  134.5+ ft.   14.  178.044+ ft. 


5. 
9. 
13 

6. 
4. 


Page  162.- 

56.568+  rd. 
18.027+  ft. 

58.309+ rd. 
1.  7.93+ ft. 
27  yd.   7. 


-1.  14.142+ ft.   2. 

6.  91.923+  rd. 

10.  23.323+  ft. 

14.  119.268+ rd. 

2.  13.22+ ft.   3. 

45  ft.   8.  41.23  ft. 


21.213+ ft.  3.  42.426+ ft.  4.  70.71+ ft. 
7.  127.278+ yd.  8.  141.421+ yd. 
11.  32.311+  yd.     12.  42.720+  yd. 


33.54+ ft. 
9.   80  rd. 


4.   11.18+ yd.       5.  13.266+ rd. 


Pagel63,—  1.  15  ft.,  10.816+ ft.  3. 

$528.       5.   196.977+ ft.       6.    31.622+ ft. 


Boy,  112.5  rd.  ;  father,  157.5  rd. 


Page  164.- 
10.   15  ft.       11^ 


-7.    12  ft. 
101.935+  ft. 


8.   240.865+  miles.  9.    17  ft.  2  in.,  approx. 


Page  166.  —  1. 

5.  84.8232  rd. 
9.  28.90272  yd. 
13.  64.4028  yd. 

9.676128  rd. 

31.416  ft. 

21.9912  ft. 

98.9604  yd. 

44  in.    34. 


17. 
21. 
25. 

29. 
33. 
38. 
43. 


47.124  in.   2.  62.832  in. 

6.  8.48232  in.  7. 

10.  26.7036  rd.  11 

14.  98.64624  rd.  15. 

18.  5.4978  yd.  19. 

22.  47.124  ft.  23 

26.  30.3688  ft.  27. 

30.  790.1124  yd.  31. 


88  in. 


35 


118.8  yd. 
3.26f  yd. 


39. 

44. 


446f  ft. 


110  in 
40. 


35.89J 


rd. 


795f  ft 


3.  131.9472  in 
11.62392  ft. 
67.23024  ft. 
16.4934  rd. 
159.90744  rd. 
.  58.1196  ft. 
,  23.0384  yd. 
823.41336  rd. 
36.  133.5f  in. 
41.  143  yd. 


4.  106.8144  ft. 

8.  18.22128  ft. 

12.  42.4116  yd. 

16.  16.084992  yd. 

20.  472.8108  yd. 

24.  65.9736  ft. 

28.  34.8432  rd. 

32.  1573.9416  ft. 

37.  78.8§  ft. 

42.  1.364  ft. 


5 

9. 

13. 

17. 

21. 

24. 

27. 

30. 

33. 

36. 

39. 

42. 


168.  — 1. 

y  sq.  in. 


Page 

2828^ 
51,492^  sq.  in 

260.26  sq.  ft. 

88.28^  sq.  ft. 

452.3904  sq. 

3216.9984  sq. 

81.713016  sq. 

254.4696  sq. 

47.783736  sq. 

55.417824  sq. 

13.854456  sq. 


245.0448  sq.  ft. 


154  sq.  in.   2.  314|  sq.  in.   3.  616  sq.  in 
6.  186.34  sq.  in.    7.  98.56  sq.  in. 

10.  69,774f  sq.  in.    11.  .0616  sq.  ft. 
14.  679.14  sq.  in.   15.  138,600  sq.  in. 
18.  116.94f  sq.  ft.   19.  211.32f  sq.  ft. 
in.      22.  804.2496  sq.  in.      23. 
in.      25.  3019.0776  sq.  ft.      26. 
ft.      28.  167.415864  sq.  ft.      29. 
in.       31.  153.9384  sq.  ft.       32. 
ft.     34.  25.517646  sq.  ft.      35.  2922.4734 
yd.       37.  176.715  sq.  in.       38.  78.54 
ft.        40.  1590.435  sq.  ft.        41.  2.18 


4.  1386  sq.  in 

8.  58.11f  sq.  in 

12.  24.64  sq.  ft 

16.  19.64J.sq.  ft 

20.  301.84  sq 

2463.0144  sq. 

55.417824 

113.0976 

283.5294 


sq. 
.sq. 
sq. 
sq. 
sq. 
sq. 


.ft. 
in. 
ft. 
in. 
ft. 

in. 
ft. 


1.  $26.45.    2.  155,000.    3.  $44,077.13.    4.  §377.73. 


Page  169. 
5.  $1441.98. 

Page  171.  — 1.  80cu.  in.  2.  120  cu.  in.  3.  144  cu.  in.  4.  128  cu.  in. 
5.  720  cu,  in.  6.  1680  cu.  in.  7.  1584  cu.  in.  8.  450  cu.  in.  9.  168 
cu.  in.   10,  465.75  cu.  in.   11.  33i  cu.  ft.   12.  49^2  cu.  ft.   13.  69i  cju.  ft. 


296  ANSWERS 

14.  113.72  cu.  ft.  15.  1099.56  cu.  in.  16.  4071.5136  cu.  in.  17.  1206.3744 
cu.  in.  18.  150.7968  cu.  ft.  19.  565.488  cu.  ft.  20.  622.0368  cu.  It. 
21.  19.5477  cu.  ft.  22.  67.593  cu.  ft.  23.  141.4883  cu.  ft.  24.  224.0026ii5 
cu.  ft.      25.    530.145  cu.  ft.       26.    1090.626075  cu.  ft. 

Page  172.  —  1.    1570.8  cu.  ft.        2.    1884.96  cu.  ft.        3.   2714.3424  cu.  ft. 
4.    3392.9280  cu.  ft.       5.    4241.16  cu.  ft.       6.   6031.872  cu.  ft. 

Page  173.  — 7.   72  T.       8.    90  T.       9.    120  T.       10.    150  T.       11.   210  T. 

12.  270  T.         13.    300  T.         14.   390  T.  15.    166+ days.  16.    150+ days. 

17.  176+ days.       18.   147+ days.       19.   129+ days.      20.  149.4  T. 

Page  174.  —  1.   2272   cu.    in.            2.    4389   cu.   in.            3.  8085   cu.   in. 

4.  53.760.5  cu.  in.  5.  68,813.4  cu.  in.  6.  96,768.9  cu.  in.  7.  189  cu.  ft. 
8.  268.8  cu.  ft.       9.  504  cu.  ft.       10.  14f  cu.  ft.       11.  22  cu.  ft.  12.  28  cu.  ft. 

13.  337.5  gal.          14.   525  gal.          15.   682.5  gal.          16.    5  gal.  17.  6  gal. 

18.  TOfiral.         19.   937.5  1b.         20.    125  1b.         21.   31501b.  22.   128.5  bu. 

23.  120.5  bu.  24.  241.06  bu.  25.  462.8  bu.  26.  674.9  bu.  27.  1542.7  bn. 
28.  900  gal.  29.  1800  gal.  30.  4320  gal.  31.  2880  gal.  32.  10,080  gal. 
33.  13.200  gal.  34.  45.7  bbl.  35.  83.3  bbl.  36.  120  bbl.  37.  160  bbl. 
38.  411.4  bbl.  39.  1097.1  bbl.  40.  14.93+  cu.  ft.  41.  34.84+  cu.  ft. 
42.  56.0+  cu.  ft.  43.  80.88  cu.  ft.  44.  89.60+  cu.  ft.  45.  124.44+  cu.  ft. 
46,  149.33+  cu.  ft.  47.  311.11+  cu.  ft.  48.  448.0+  cu.  ft.  49.  653.33+  cu.  ft. 
50.  6972.6  lb.  51.  14849.681+  lb.  52.  70,000  lb.  53.  140,683.59  lb. 
54*  318,087  gal.  55.  659.736  gal.  56.  1178.1  gal.  67.  848.23  gal. 
58.   7068.6  gal.       59.   11,875.248  gal.        60.    28,627.83  gal.        61.    37,699.2  gal. 

Page  178.  — 2.   $75.96. 

Page  179.  — 3.    $18.96,  $29.44,  $9.44. 

Page  181.  — 1.   15.60.      2.  $8.95.       3.  $11.20.      4.  $9.24.       5.  $141.75. 
6.   $19.59.  7.    $3.70.  8.    $109.55.  9.    $125.35.  10.    $157.51. 

12.    $340.95. 

Page  184. —  1.   $.14.      2.    $.55.       3.   $.161ess.      4.   $2.78. 

Page  186.— 1.   $16.       2.    $27.       3.    $26.67.       4.    $31.25.  5.    $78.75. 

6.   $168.75.       7.    $125.       8.    $300.       9.    $500.        10.    $962.50.  11.    $1000. 

12.    $980.       13.    $67.50.       14.    $208.25.       15.  $465.       16.  $500.  17.  $480. 

18.   $875.       19.   $32.        20.    $54.        21.    $70.50.        22.   $86.40.  23.    $110. 

24.  $140.  25.  $300.  26.  $324.  27.  $220.50.  28.  $275.  29.  $360. 
30.   $843.75. 

Page  187.  — 1.    $18.      2.   $15.       3.    $11.25.       4.  33^%.       5.   $12,000. 
6.    $12.'     7.    $20.       8.    $13,500.      9.    $517.50. 

Page  190.-1.    $40.28.  2.    $144.09.  3.    $114.25.  4.   $240.56. 

5.  $487.10.  6.  $180.85.  7.  $95.08.  8.  $92.82.  9.  $68.55. 
10.    $146.13.        11.    $456.90.        12.   $605.10.       13.   $464.10.        14.    $536.40. 

Page  191.— 15.   $640.38.         16.    $1275.20.         17.    $102.40,  $2452.40. 

Page  193.— 1.   $3.60.        2.    $6.30.         3.   $9.60.        4.    $14.         5.    $12. 

6.  $6.25.       7.    $11.25.      8.    $30.       9.    $48.75.       10.    $90. 

Page  194. —1.    1^  mills.  2.    2  mills.  3.   2 Jf  mills.  4.   3  mills. 

5.   3  mills.  6.   2^  mills.  7.    3f  mills.  8.   4|  mills.    '       9.    4  mills. 

10.   3/^  mills. 


ANSWERS  297 

1.    $4000.  2.    §5000.  3.    $10,000.  4.   87500.  5.    S4500. 

6.    $50,000.         7.    $60,000.        8.   $45,800.        9.   $42,763.16.        10.    $58,450. 

Page  195. —1.    $1.24.  2.   $1.37.       3.    $1.42.      4.    $1.56.  5.  $1.63. 

6.   $1.98.        7.   $2.40.        8.  $3.12.        9.    $3.47.        10.   $3.96.  11.  S5.78. 

12.    $6.44.             13.    $7.02.  14.    $7.59.             15.    $7.97.  16.  $9.24. 

17.  $10.32.         18.   $12.38.  19.   $14.40.        20.    $15.60. 

Page  196. —  1.   2 1  mills.        2.   3i  mills. 

Page  197.  — 3.   4f  mills.  4.   4  mills.  5.   $60,  $69.76.  6.  13.21 

mills,  $165.13         7.    $115.87.        9.    $94.76. 

Page  198.  — 10.   $4750. 

Page  199.-1.   $78.        2.   $115  gain. 

Page  204. —1.   $4515.          2.    $2415.            3.   $19,030.  4.  $30,040. 

5.    $16,530.          6.    $29,537.50.          7.    $5965.          8.   $22,480.  9.  $17,370. 

10.    $43,893.75.        11.   $32,910.        12.    $30,495.        13.    $7350.  14.  $45,885. 

15.   $103,635.              16.    $16,808.75.              17.    $21,096.25.  18.  $84,780 

19.   $29,936.25.             20.    $34,012.50.              21.   $63,840.  22.  $44,775. 

23.  $181,575.         24.    $142,050. 

Page  205.  — 1.    $8085.      '      2.    $16,680.  3.    $1835.  4.    $18,480. 

5.    $6145.  6.    $7020.  7.   $10,252.50.  8.    $9270.  9.    $5868.75. 

10.    $30,060.        11.   $24,480.       12.   $25,322.50.       13.    $56,020.       14.    $6290. 
15.   $6550.  16.    $19,057.50.  17.   $43,917.50.  18.    $60,660. 

19.  $74,445.       20.    $47,380.       21.    $52,100.       22.    $160,200.      23.   $348,300. 

24.  $375,437.50. 

Page  206.  — 1.    $241.50.         2.   $1728.         3.   $4513.50.         4.    $1382.50. 

5.  $7848.75.  6.    $5662.  7.    $14,570.  8.    $11,265.  9.   $14,370. 
10.   $10,802.50.        11.    $1440.        12.    $22,511.25.       13.    $30,440.       14.    $857. 

15.  $3619.       16.    $7502.50.       17.    $8388.75.        18.    $267.50.        19.    $10,435. 

20.  $9047.50.  21.    $5470.  22.   $44,902.50.  23.   $45,237.50. 
24.    $70,475.         25.    $80,600.          26.    $76,650. 

Page  207.  — 1.    $660  gain.             2.  $728.75  gain.  3.   $6747.50  loss. 

4.   $145  gain.              5.    $  1320  gain.  6.   $6335  loss.  7.    S  1830  loss. 

8.    $4405  loss.           9.    $3397.50  gain.  10.    $885£rain.  11.    $3925  gain. 

12.  $2840  loss.       13.    $13,117.50  gain.  14.   $14,700  gain.  15.    $8575  gain. 

16.  $38,950  gain. 

Page  209.-1.   49,  $119.77  uninvested.  2.   2207,  $  13.70  uninvested. 

3.   99,  $60.27  uninvested.  4.    199,  $80.65  uninvested.  5.    400,  $40 

uninvested.  6.    281,  $15.35  uninvested.  7.    84,  $97.20  uninvested. 

8.    174,  $75.40  uninvested.  9.    232,  $15.20  uninvested.  10.    176,  $85.60 

uninvested.  11.    201,  $40.72  uninvested.  12.   199,  $  73.52  uninvested. 

13.  101,  $9.72  uninvested. 

Page  210.— 1.    6f%.  2.   5%.         3.  4%.         4.   4|  %.         5.   5f^o. 

6.  5ffo.  7.    5%.  8.    5%.  9.   4.1%.  10.   4.93+%.         11.    5%. 
12.    5f%.       13.   4.73+%.       14.    4.32+%.       15.   3.69+%. 

Page  211.  — 16.   First,  .24%.  17.   The  same.  18.    $36  gain. 

19.    $395  gain.         20.    $  1850  ;  1st ;  1st,  8.07+ %  more.  21.    $400,7.97+%. 

22.    $138.75,  .8%.         23.   1st,  $170. 


298 


ANSWERS 


Page  215. 

Rent 
1240 
300 


1. 

2. 

3. 

4 

5. 

6. 

7. 

8. 

9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 


820 
360 
260 
280 
320 
340 
400 
440 
480 
500 
640 
560 
600 
700 


1. 
3. 


Food 
$420 

525 

560 

540 

455 

490 

560 

595 

600 

660 

720 

750 

810 

840 

750 

875 

$310. 


$80. 
.  $9.60.   i 

■  4.  $33.60. 


Clothing 
$180 
225 
240 
270 
]95 
210 
240 
255 
300 
330 
360 
375 
405 
420 
600 
700 

2.   $295. 

4.   $50. 


Misc. 

$300 
375 
400 
450 
325 
350 
400 
425 
500 
550 
480 
500 
540 
560 
450 
525 


Savins 

$  60 

75 

80 

180 

65 

70 

80 

85 

200 

220 

360 

375 

405 

420 

600 

700 


5.    $221. 

$  12  (walls  only). 

5.   $55.51.  6. 


$175.30. 


7.    $247.26. 


Page  216. 

Page  217. 

1.   $240. 

Page  218. 
8.    $110.70. 

Page220.  — 13.    $2.31.  14.    $.21.  15.    $2.96,  $2.08,  $1.76,  $.72, 

$1.04,  $8.56. 

Page  221. 

5.   980  watts. 


-1.   75  watts.      2.    120  watts.      3.   450  watts.      4.  1125  watts. 
6.    1095  watts.       7.    $1.08.       8.    $3.29.      9.   $2.17. 


Page  222.  — 1. 

6.   Gas  stove.      7. 


6. 


Page  223. 

$8.25.      7. 

Page  224. 

1.   Uft.       I 


$9.90.      2.   33|lb.      3.    25|  bu.      4.  3:20.       5.   $46.80. 
$16.39  ;  27iVo^  (cost  of  can  included). 

-1.    $.90.        2.   $1.75.        3.  $4.68.        4.  $.30.        5.    $.33|. 

$.20. 


8.   $3.04. 

$.20.       3.   Second. 


Page  225.— 5. 

Page  233.  — 1. 
5.  378  sq.  in.  6. 
10. 


$.45i 


?' 


$.08. 


4.    $4.65,  $.58 J. 
$1.70.       7.   $2.35. 


35  sq. 


14. 
18. 
22. 
26. 
30. 
35. 
39. 


75|  sq. 
106if 


ft. 
sq.  ft. 
864  sq.  in. 
54  sq.  ft. 
630  sq.  ft. 
16  sq.  ft.       31. 
61|  sq.  ft. 
313}|  sq.  ft. 


8^sq, 


in.   2.  120  sq, 
ft.    7.  14  sq. 
li.  75  sq.  ft. 
15.  202|f  sq.  ft. 
19.  1200  sq.  in. 
23.  1811  sq.  ft. 
'>•*  1166f  sq.  ft. 

ft.   32.  109  sq, 


,  in. 
ft. 
12 
16. 
20. 
24. 
28. 
ft. 


3.  180  sq, 
8.  18^  sq. 
92  sq.  ft. 
280  sq.  in. 
llf  sq.  ft. 
248  sq.  ft. 
lOf  sq.  ft. 


in. 

ft. 


Page  234.  —  1.  60  cu.  in. 

450  cu.  in.      6.  1152  cu 


27 

56f  sq.  It.  az.  luy  sq.  n.   aiij.  /: 

36.  90f f  sq.  ft.  37.  94||  sq.  : 

40.  380^1  sq.ft.  41.  354f|  sq.  ft. 


33.  72|  sq.  ft. 
ft. 


2.  105  cu.  in.   3.  144  cu.  in. 
in.      7.  1944  cu.  in. 


4.  320  sq.  in. 

9.  361  sq.  ft. 

13.  84  sq.  ft. 

17.  540  sq.  in. 

21.  19i  sq.  ft. 

25.  452  sq.  ft. 

29.  16i  sq.  ft. 

34.  97  sq.  ft. 

38.  2621  sq.  ft. 

4.  240cu.  in. 
8.  9072  cu.  in. 


ANSWERS                                        299 

9. 

160  cu.  ft.               10.   216  cu.  ft.              11.    300  cu.  ft.              12.   432  cu.  ft. 

13. 

1200  cu.  in.           14.   4050  cu.  in.          15.   6144  cu.  in,           16.    8100  cu.  in. 

17. 

20cu.  ft.       18.  31^  cu.  ft.       19.  .33f  cu.  ft.       20.  96  cu.  ft.       21.  85|cu.  ft. 

22. 

3851  cu.  ft.           23.   601|  cu.  ft.           24.    1560|  cu.  ft.           25.   360  cu.  in. 

26. 

540  cu.  in.             27.    800  cu.  in.             28.    1470  cu.  in.             29.    120  cu.  ft. 

30. 

1.50  cu.  ft.      31.  144  cu.  ft.      32.  150  cu.  ft.       33.  21  cu.  ft.      34.  22  cu.ft. 

35. 

291  cu.  ft.       36.   47^  cu.  ft. 

Page  236.  — 1.  150  sq.  in.  2.  432  .sq.  in.  3.  600  sq.  in.  4.  840  .sq.  in. 
5.  270sq.  in.  6.  540  .sq.  in.  7.  972  sq.  in.  8.  IH  .sq.  ft.  9.  12.5664  sq.ft. 
10.  .37.6992  sq.ft.  11.  25.556  sq.ft.  12.  56.5488sq.ft.  13.  791.6832  .sq.  in. 
14.  1.306.9056  sq.  in.  15.  2199.12  sq.  in.  16.  3166.7328  .sq.  in. 
17.  49.0875  .sq.  ft.   18.  133.518  sq.  ft. 

1.  150  cu.  in.  2.  216  cu.  in.  3.  300  cu.  in.  4.  320  cu.  in. 
5.  432  cu.  in.  6.  6  cu.  ft.  7.  10  cu.  ft.  8.  12  cu.  ft.  9.  20  cu.  ft. 
10.  30  cu.ft.     11.  5.25  cu.ft.     12.  10.2  cu.  ft.     13.  17.5666  cu.  ft. 

14.  20.25  cu.  ft.   15.  49.4666  cu.  ft. 

Page  237.  — 16.    502.656  cu.  in.       17.   424.116  cu.  in.       18.  942.48  cu.  in. 

19.  1696.464   cu.    in.  20.    4580.4528   cu.    in.  21.   43.9824   cu.   ft. 

22.  11.5192  cu.  ft.  23.  53.4072  cu.  ft.  24.  9.8175  cu.  ft.  25.  35.343  cu.  ft. 
26.  17.180625  cu.  ft.  27.  25.9182  cu.  ft.  28.  43.295175  cu.  ft. 
29.    115.42471+  cu.  ft.       30.    262.9781  cu.  ft. 

Page  238.  —  1.    75  sq.  in.  2.   96  sq.  in.  3.    135  sq.  in.  4.   170  .sq.  in. 

5.    216  sq.  in.         6.    1^  sq.  ft.  7.    3  sq.  ft.  8.    5  sq.  ft.  9.    Q\  sq.  ft. 

10.    9  sq.ft.       11.   4f  sq.ft.  12.    2*- sq.  ft.  13.    6/..  sq.  ft.  14.    12f  s(i.  ft. 

15.  17^  sq.ft.      16.  240sq.  in.  17.  288  sq.  in.  18.  360sq.  in.  19.  480.sq.  in. 

20.  864  sq.  in.       21.   20  sq.  ft. 

Page239.  —  22.  9  sq.  ft.  23.  4^  sq.  f t.  24.  llf  sq.  ft.  25.  12  sq.  ft. 
26.  6|  sq.  ft.  27.  9i  sq.  ft.  28.  18i  sq.  ft.   29.  35^|  sq.  ft.   30.  46f  sq.  ft. 

Page  240. —1.  24  sq.  in.   2.  28  sq.  in.    3.  22^  sq.  in.  4.  27  sq.  in. 

5.  40  sq.  in.    6.  f  sq.  ft.    7.  1^  sq.  ft.    8.  lj\  sq.  ft.  9.  1|  sq.  ft. 

10.  2|  sq.  ft.   11.  2}i  sq.  ft.   12.  4i7^  sq.  ft.   13.  8^  sq.  ft.  14.  6.69  sq.  ft. 

15.  14.29  sq.ft.   16.  18.8496  sq.  in.  "17.  37.6992  .sq.  in.   18.  56.5488  sq.  in. 

19.  141.372  sq.  in.   20.  179.071  sq.  in.   21.  791.6832  sq.  in.   22.  942. 48. sq.  in. 

23.  1244.0736  sq.  in.  24.  1130.976  sq.  in.  25.  3392.928  sq.  in. 
26.  1099.56  sq.  in.  27.  2387.616  sq.  in.  28.  4241.16  sq.  in. 
29.  8372.-364  sq.  in.   30.  10555.776  sq.  in. 

Page  241. —  1.  180  cu.  in.   2.  540  cu.  in.   3.  756  cu. 
5.  10|  cu.  ft.     6.  18.75  cu.  ft.     7.  3.125  cu.  ft. 
9.  16.245+  cu.  ft.        10.  565.488  cu.  in.        11, 
12.  2544.696  cu.  in.   13.  2.618  cu.  ft.   14.  7.65765  cu.  ft. 

16.  1.84078125  cu.  ft.   17.  3.337+  cu.  ft.   18.  2.6761  cu.  ft. 

20.  8.062+  cu.  ft.   21.  6.4141+  cu.  ft.  . 

Page  243. —1.  50.2656  sq.  in.  2.  113.0976  sq.  in. 

4.  2.1816  sq.ft.    5.  3.1416  sq.  ft.  6.  5.585  sq.  ft. 

8.  15.2053  sq.  ft.  9.  28.2744  sq.  ft.  10.  32.1699  sq.  ft. 

12.  19.635  sq.ft.    13.  2.1816  sq.  ft.  14.  4.276  sq.  ft. 

16.  7.0686  sq.ft.    17.  8.7266  sq.  ft.  18.  11.541  sq.  ft. 

20.  4.9087  .sq.  ft.    21.  5.585  sq.  ft.  22.  7.8758  sq.  ft. 


in. 

4-  i 

cu. 

ft. 

8. 

6.9375  cu. 

ft. 

13 

40.416   cu. 

ft. 

15. 

5.30145 

cu. 

ft. 

19 

.  1.959+ 

cu. 

ft. 

3. 

1.3962 

sq. 

ft. 

7. 

12.5664 

sq. 

ft. 

11. 

40.7151 

sq. 

ft. 

15. 

4.9087 

sq. 

ft. 

19.    4.276 

sq. 

ft. 

23. 

9.6211 

sq. 

ft. 

300  ANSAVERS 

24.  10.5592  sq.  ft.  25.  904.7808  sq.  ft.  26.  Earth,  201,062,400  sq.  mi.  ; 
Jupiter,  24,328,550,400  sq.  mi. 

Page  244.  — 1.    4.1888  cii.  in.        2.    33.5104  en.  in.        3.    113.0976  cu.  in. 
4.   268.0832  cu.  in.         5.    523.6  cu.  in.         6.   4.1888  cu.  ft.         7.    7.2382  cu.  ft. 

8.  14.1372  cu.  ft.  9.  24.429  cu.  ft.  10.  8.18125  cu.  ft.  11.  65.45  cu.  in. 
12.  268.0832  cu.  in.  13.  381.7044  cu.  in.  14.  696.9116  cu.  in. 
15.    1160.3492  cu.  in.       16.  1.0226  cu.  ft.       17.  1.2411  cu.  ft.       18.  2.424  cu.  ft. 

19.  5.9641  cu.  ft.       20.    8.181  cu.  ft. 

Page  250.  — 1.    $314.67.      2.   $79.85. 

Page  251.  — 3.   $145.31.      4.   $1437.96.      5.   $290.04.      6.   $57.35. 

Page  252. —  1.   $227.87.      2.   $94.80.       3.   $105.54.       4.    $527.16. 

Page  255.  — 1.    15°.       2.    55°.      3.   30°.       4.    80°.        5.   115°.        6.   120°. 
7.    75^.        8.   90°.        9.   90°.         10.    90°.       11.    150°.         12.    167°.         13.    67°. 

14.  45°.  15.    95°.  16.    112°.  17.   45°.  18.    118°.  19.    14°  45'. 

20.  64°  50'.  21.  15°.  22.  70°  25'.  23.  53°  15'.  24.  71°  2'.  25.  33° 
64'  10".   26.  34°  48'  57".   27.  2°  58'  54".   28.  73°  54'  36". 

Page  257.  —  1.  35  min.,  52|  sec.  2.  4  hr.,  55  min.,  38f  sec.  3.  39  min.,  5i  sec. 
4.  54  min.,  25f  sec.   5.  1  lir.,  51  min.,  39f  sec.   6.  3  hr.,  13  min.,  41^  sec. 

Page  258.-7.   2  hr.,  19  min.,  15f  sec.  8.    5  hr.,  5  min.,  22^^^  sec. 

9.  7  lir..  33  min.,  29^  sec.  10.  9  hr.,  9  min.,  37x^3  sec.  11.  2  hr.,  15  min., 
36|sec.  12.  21n:.,3min.,50|sec.  13.  Ihr.,  39 min.,  44 sec.  14.  Ihr.,  6min., 
11|  sec.  15.   8  hr.,  25  min.,  69|  sec.  16.   2  hr.,  42  min.,  2^-^  sec. 

17.  1  hr.,  45  min.,  52  sec.  18.  9  min.,  44^^^  sec.  19.  12  hr.,  59  min., 
64  sec.  20.  6  hr.,  59  min.,  284  sec.  21.  8  hr.,  19  min.,  m  sec.  22.  14  hr., 
35  min..  55|f  sec.  23.  42  min.  \^  sec.  before  12,  noon.  24.  8  min.  20f  sec. 
after  10,  a.m.  25.  11  min.  55|  sec.  before  12,  noon.  26.  23  min.  57 ^^  sec. 
after  12,  noon.  27.  12  min.  4|  sec.  before  11,  p.m.  28.  1  min.  30f  sec. 
before  9,  a.m.  29.  5  lir. 7  min.  49|  sec. after  12,  noon.  30.  27  min.  lOy^^  sec. 
before  10  p.  m.     31.  41  min.  18f  sec.  before  12,  midnight. 

Page  259.  — 1.   47°  3'  6"  W.  2.    32°  3'  6"  W.  3.   9°  33'  6"  W. 

4.  24^  11'  54"  E.  5.  50°  26'  64"  E.  6.  87°  56'  54"  E.  7.  107°  3' 
6"  W.  8.  118°  18'  6"  W.  9.  144°  33'  6"  W.  10.  169°  33'  6"  W. 
11.  162°  3'  6"  W.  12.  162°  56'  54"  E.  13.  28°  14'  21"  W.  14.  56°  51' 
51"  W.           15.    119°  25'  36"  W.           16.   76°  53'  9"  E.           17.   91°  49'  24"  E. 

18.  97°  49'  24"  E.  19.  5  min.  22/^  sec.  before  10  a.m.  ;  76°  20'  38". 
20.    12°  26'  53"  E. 

Page  264. —1.    5000  m.  2.   3500  m.         3.    15,000  m.         4,  21,700  m. 

5.  15,080  m.  6.    600  m.  7.    450  m.  8.    180  m.  9.    123  m. 

10.  111.5  m.  11.    12.5  m.  12.    1.25  m.  13.    .125  m.  14.    1.75  m. 

15.  14.5  m.  16.  2.4  m.  17.  .3546  m.  18.  .1175  m.  19.  1.175  m. 
20.  14.05  m.  21.   3500  m.          22.    580  m.          23.   4040  m.  24.  4.5  m. 

25.  15.8  m.  26.  35.25  m.  27.  4.95  m.  28.  2.07  m.  29.  7.75  m. 
30.  3.048+ m.  31.  9.753+ m.  32.  1.706+ m.  33.  .901+ m.  34.  2.794+ m. 
35.  .749+ m.  36.  39.37+ ft.  37.  51.67+ ft.  38.  159.94+ ft 
%%.  82.02+  It.  40.  820.20+  ft.  41.  36.9093+  ft.  '  42.  2.4856  mi. 
43.  7.7676  mi.  44.  6.5247  mi.  45.  77.9857  mi.  46.  160.926  Km. 
47.  201.125  Km.        48.    .0102  Km.        49.    .00201  Km. 


ANSWERS  301 

Page  266. —1.  125,000,000  sq.m.  2.  1,600,000  sq.  m.  3.  25,000  sq.m. 
4.  124,600,000  sq.  m.  5.  3,752,-500  sq.  m.  6.  125,005  sq.  m.  7.  .015625 
sq.  m.  8.  2.54  sq.m.  9.  1545  sq.m.  10.  119.6  sq.  yd.  11.  13,754  sq.  yd. 
12.  1.3455  sq.  yd.  13.  149,500  sq.  yd.  14.  4.825  sq.  mi.  15.  9.3026  sq.  mi. 
16.    .004825  sq.  mi.         17.    .00439075  sq.  mi. 

Page  268.  —  1.    1.5  cu.  dm.,  150  cu.  dm.  or  .15  cu.  m.  2.   35  cu.  cm., 

125  cu.  m.       3.   4570  cu.  cm.  or  4.57  cu.  dm.,  12,-575  cu.  cm.  or  12.-575  cu.  dm. 

4.  15,000  cu.  dm.  or  1-5,000,000  cu.  cm..  1-50,000  cu.  cm.  5.  275,000  cu.  dm. 
or  275,000,000  cu.  cm.,  4,-500,000  cu.  cm.  6.  15,750,000  cu.  mm.,  354,000,000 
cu.  mm. 

Page  269.  —1.  1.5  Dl.  2.  1.25  Dl.  3.  -50  dl.  or  5  1.  4.  -3-50  cl.,  35  dl., 
3.5  1.  5.  25.475  1.  or  2.5475  Dl.  6.  25.475  HI.  or  2.-5475  Kl.  7  .3-50  HI. 
8.    458  Dl.      9.    1752.51.  10.    1475  dl.  11.    351.25  dl.  or -3-512.5  cl.  or 

35,125  ml.  12.  4-52.5  ml.  13.  10.-567  qt.  14.  13.2087  qt.  15.  185.1-3-38  qt. 
16.    1.585+ qt.  17.    147,9-38  qt.  18.    27,262.86  qt.  19.   31.78  qt. 

20.    14.3464  qt.  21.    22.7681  qt.  22.    15.89  qt.  23.   228.135  qt. 

24.    136.2  qt.  25.  15.60625  bu.  26.   34.333  bu.  27.   4.9656  bu. 

28.   70.9-375  bu.  29.    5.286  HI.  30.   26.607  HI.  31.    28.193  HI. 

32.    17.621  HI. 

Page  270. —  1.   12,000  g.  2.    1-5,-500  g.  3.    1750  g.  4.    7580  g. 

5.  1571  g.       6.    154,2.50  g.        7.    1.5  g.        8.    17.5  g.       9.    375  g.       10.    17.5  g. 

11.  187.5  g.  12.  1875  g.  13.33.0693  1b.  14.2.75577  1b.  15.  27.5577  1b. 
16.    .2755  1b.  17.   34.6345  1b.  18.   346.3458  1b.  19.    .7744  1b. 

20.  2.6455  1b. 

Page  272.  — 1.    780  Kg.       2.   2316  Kg.        3.    133.1  Kg.       4.  1,130,000  g. 

6.  627,500  g.  6.  88,000  g.  7.  1,768,450  g.  8.  6,658,500  g.  9.  3-500  g. 
10.  112,500,000  g.  11.  1,975,000  Kg.  12.  92,000  Kg.  13.  138,000  Kg. 
14.    158,000  Kg.       15.    10,500,000  g.       16.    26,250  g. 

Page  273. —1.   .27559  in.      2.  65.178675  Km.       3.8540  m.      4.  S  20.10+. 

6.  360  sq.  m.,  3876.04  sq.  ft.  6.  4535.9  metric  tons.  7.  2,644,448.9+  cu.  m. 
8.   84-54 bottles.      9.  30.48  m.,  .03048  Km.      10.  71,122.912+ Kg.      11.  S  533.64. 

12.  56.7816  1.       13.    1312+ steps. 

Page  274.  — 14.  10,000  capsules.  15.  5319.1656834  Km., -5319165.6834  m. 
16.  29.7375  Kg.  17.  !$  9.37  approx.  18.  1817.0112  Kg.  19.  39.095  francs, 
or  3909.5+  centimes.  20.  28.39725  miles.  21.  33  ft.  2.62  in.  22.  6.67  ft. 
23.    126.25  1.,  33.352+ gal. 

Page  275.  —24.  358+  turns.  25.  27  Kg.  Copper,  18  Kg.  Zinc.  26.  S  15.59. 
27.  137.362+1.,  145.150-^  qt.    28.   289.9248  Kg.,  639.168+ lb.  29.    6.8+ Km. 

30.    $5.54. 

Page  282.  — 1.   15.          2.   21.          3.    31.          4.    38.          5.   36.  6.   41. 

7.  43.  8.  44.  9.  64.  10.  68.  11.  87.  12.  98.  13.  202.  14.  199. 
16.    13.1.           16.    1.96.           17.    .17.           18.    5.21.          19.    .404.  20.    49.9. 

21.  11.44+.  22.  .30.36+.  •  23.  24.66+.  24.  2.23  +  .  25.  .18+.  26.  .09*. 
27.    .84+.         28.    .82+.         29.    .92+.         30.    .96+. 


ANNOUNCEMENT 

New  Interpretative  Readers 

Wheeler's  Graded  Literary  Readers  (With  interpretations)^ 

William  Her  Crane — William  Henry  Wheeler 

THE  successful  hunter  keeps  his  eye  on  the  game.  The  success- 
ful fisherman  baits  his  hook  to  suit  the  taste  of  the  fish  and  not 
to  suit  his  own  taste. 
The  authors  of  these  new  readers  have  kept  their  eyes  on  the 
children  at  all  times.  They  have  baited  the  books  to  suit  the  taste 
of  the  children  and  to  supply  their  present  needs. 
By  a  clear  and  helpful  interpretation  of  each  selection,  these  new 
readers  help  the  children  to  find  the  thoughts  which  lie  below  the 
surface  in  the  best  literature.  They  do  not,  however,  attempt  to 
teach  the  history  of  English  Literature.  They  simply  help  the 
children  to  read  real  literature  easily,  intelligently  and  under- 
standingly. 

The  definitions  merely  give  the  meanings  of  the  words  and  phrases 
in  the  sense  that  they  are  used  in  the  selections  and  not  the  mean- 
ings that  they  may  have  in  some  other  selections  which  the  children 
have  not  read  and  which  they  may  never  read.  These  definitions  are 
simply  "first  aids"  for  the  children  and  not  complete  dictionary 
definitions. 

The  biographies  are  brief  because  the  children  must  be  interested 
in  an  author's  writings  before  they  can  become  interested  in  his  life; 
because  it  is  infinitely  more  important  that  the  children  should  spend 
their  time  learning  to  read  and  appreciate  an  author's  writings  than 
it  is  that  they  should  learn  all  the  foolish  gossip  about  the  author 
and  all  the  petty  details  of  his  life.  Hamlet  said  "The  play's  the 
thing."  In  a  series  of  school  readers  the  life  of  the  selection,  and 
not  the  life  of  the  author,  is  the  principal  thing. 

Wheeler's  Graded  Literary  Readers  (With  interpretations) 

A  Fourth  Reader.  320  pages,  List  price.  $0.85.  A  Sixth  Reader.  400  pages.  List  price.  $0.95 
A  Fifth  Reader,  352  pages.       "       "  85.        A  Seventh  Reader.  448  pages.  "  .95 

An  Eighth  Reader,  448  pages.  List  price,  $0.95 

For  single  copies  sent  by  mail,  add  the  parcel  post  rate  to  the  list  price. 

Zones 1-2345678 

6c     8c     lie    14c    17c    21c    24c 

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616  South  Michigan  Avenue,  Chicago 


NEW     INTERPRETATIVE     READERS 


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Co"    , 

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LIBRARY 

